(Adds anti-Trump protests, paragraphs 8-9)
* New York businessman wins in first run at public office
* Republicans retain control of U.S. House, Senate
* Obama invites Trump to White House meeting on Thursday
* Protesters chant against Trump in U.S. cities
By Steve Holland and John Whitesides
Nov 9 (Reuters) - Republican Donald Trump put aside the celebrations and focused on Wednesday on his 73-day transition to the White House as rival Hillary Clinton promised to bury the bitterness of their long presidential race and work to unify a divided country.
After Trump's stunning upset of the heavily favored Clinton, Democratic President Barack Obama and leading figures in the Republican Party who had struggled to make peace with Trump all vowed to move past the campaign ugliness.
"Donald Trump is going to be our president. We owe him an open mind and the chance to lead," Clinton, the Democratic nominee, said in a concession speech in New York, joined by her husband, former President Bill Clinton, and daughter Chelsea.
While her loss was painful "and it will be for a long time," she had offered to work with Trump as he prepares to begin his four-year term on Jan. 20, Clinton told supporters.
A wealthy New York real estate developer and former reality TV host, Trump rode a wave of anger toward Washington insiders to win Tuesday's election against Clinton. A former first lady, U.S. senator and secretary of state, Clinton also ran for president in 2008.
Obama, who campaigned hard against Trump, invited him to the White House for a meeting on Thursday after a brutal night for the Democratic Party, which also fell short of recapturing majorities in both chambers of Congress.
"We are now all rooting for his success in uniting and leading the country," Obama said at the White House, adding he and his staff would work with Trump to ensure a successful transition. "We are not Democrats first, we are not Republicans first, we are Americans first."
But reflecting the bitterness of a long election campaign that often focused more on character than on policy, scattered anti-Trump protests broke out across the country, including in New York and Chicago, with demonstrators denouncing Trump's campaign rhetoric about immigrants, Muslims and other groups.
Thousands of protesters thronged Midtown Manhattan and marched toward Trump Tower on Wednesday evening, while at a park farther downtown, hundreds of people shouted: "Not my president." In Chicago, thousands gathered outside the Trump International Hotel and Tower downtown while chanting phrases like "No Trump! No KKK! No racist USA."
Trump and his senior aides met at Trump Tower in New York to begin the transition. "They are hunkered down in meetings, plotting the next steps, the transition, the first 100 days, key staff positions," said a source close to Trump's campaign.
Potential choices for his administration included Republican figures who eagerly supported Trump even when he faced opprobrium from other senior Republicans.
Possible names included Republican National Committee chair Reince Priebus as White House chief of staff, RNC spokesman Sean Spicer as White House spokesman, U.S. Senators Jeff Sessions and Bob Corker in possible roles as secretary of state or defense secretary, and former House of Representatives Speaker Newt Gingrich as secretary of state, a source close to the campaign said.
Trump will enjoy Republican majorities in both chambers of the U.S. Congress that could help him implement his legislative agenda and appoint a Supreme Court justice to fill the vacancy created by the death of conservative Justice Antonin Scalia.
In the Senate, Democrats secured a second gain on Wednesday, when Republican Senator Kelly Ayotte conceded defeat in New Hampshire to challenger Maggie Hassan, the state's Democratic governor. But the Republicans retained their majority.
"Now, Donald Trump will lead a unified Republican government and we will work hand-in-hand on a positive agenda to tackle this country's big challenges," House of Representatives Speaker Paul Ryan, who had a strained relationship with Trump, told reporters, saying Trump had earned a mandate in the election.
In an Oct. 25 Reuters interview, Trump said his top priorities when he took office would be building stronger borders, repealing Obama's national healthcare plan, aiding military veterans and working to create more jobs.
In his victory speech early on Wednesday, he also promised to embark on a project to rebuild American infrastructure and to double U.S. economic growth.
Republican Senate leader Mitch McConnell said on Wednesday that repealing the healthcare plan known as Obamacare would be a "pretty high item" on the agenda. House Democratic leader Nancy Pelosi said in a statement that she spoke to Trump about passing a "robust" jobs bill.
Worried that a Trump victory could cause economic and global uncertainty, investors initially fled stocks worldwide, but Wall Street made a dramatic turnaround and the U.S. dollar hit its highest level against the Japanese yen in nearly four months.
The Mexican peso recouped some losses after falling to a record low. The currency has been vulnerable to Trump's threats to rip up a free trade agreement with Mexico and to tax money sent home by migrants to pay to build a border wall.
Speaking to cheering supporters after his victory, Trump said it was time to heal divisions. "It is time for us to come together as one united people," Trump said. "I will be president for all Americans," he said, praising Clinton for her service.
His comments departed sharply from his campaign rhetoric in which he repeatedly branded Clinton as "Crooked Hillary" amid supporters' chants of "lock her up."
Trump's campaign manager, Kellyanne Conway, did not rule out on Wednesday the appointment of a special prosecutor to investigate Clinton's past conduct, a threat Trump made in an election debate last month.
Obama spokesman Josh Earnest said the White House hoped the tradition of not using the criminal justice system to exact revenge on political opponents would continue under Trump.
Senior House Republican Jason Chaffetz plans to continue investigating Clinton's use of a private rather than government email server while she was secretary of state, a Chaffetz aide said. FBI Director James Comey has said a year-long probe by the agency into the setup revealed nothing to merit criminal charges.
Despite losing the state-by-state electoral battle that determines the U.S. presidency, Clinton narrowly led Trump in the nationwide popular vote, according to U.S. media tallies.
Fueling his upset win was Trump's avid support among white non-college educated workers. He ran up big leads in rural areas, beating Clinton by 27 percentage points among voters outside of urban areas, a Reuters/Ipsos Election Day poll found.
While Clinton, 69, won Hispanics and black and young voters, she did not win those groups by greater margins than Obama did in 2012. Younger blacks did not support Clinton like they did Obama. She won eight of 10 black voters between the ages of 35 and 54. Obama won almost 100 percent of those voters in 2012.
At 70, Trump will be the oldest first-term U.S. president. The presidency will be Trump's first elected office, and it remains to be seen how he will work with Congress. During the campaign, Trump was the target of sharp disapproval, not just from Democrats but from many in his own party.
GOOD NEWS FOR RUSSIA
Foreign leaders pledged to work with Trump, but some officials expressed alarm the vote could mark the end of an era in which Washington promoted democratic values and was seen by its allies as a guarantor of peace.
During the campaign, Trump expressed admiration for Russian President Vladimir Putin, questioned central tenets of the NATO military alliance and suggested that Japan and South Korea should develop nuclear weapons to shoulder their own defense burden.
Russia and Putin appeared to be winners from Trump's victory. Defying years of U.S. foreign policy orthodoxy, the Republican had promised much warmer relations with Moscow, despite Russia's intervention in the Syrian civil war and its seizure of Ukraine's Crimea region.
Russia's parliament erupted in applause after a lawmaker announced that Trump had been elected, and Putin told foreign ambassadors he was ready to fully restore ties with Washington.
Russia is hoping that improved relations could yield an elusive prize: the lifting or easing of sanctions imposed by the United States and the European Union to punish Moscow for its 2014 annexation of Crimea and support for separatists in eastern Ukraine.
Israeli Prime Minister Benjamin Netanyahu, who sparred with Obama, spoke by phone to Trump, who proposed they meet "at the first opportunity," Netanyahu's office said. Chinese President Xi Jinping said Beijing and Washington shared responsibility for promoting global development and prosperity.
Iran urged Trump to stay committed to the nuclear accord between Tehran and world powers, which Trump has sharply criticized. Several authoritarian and right-wing leaders hailed Trump's victory.
Other officials abroad, some with senior roles in government, took the unusual step of denouncing the outcome, calling it a worrying signal for liberal democracy and tolerance in the world.
"Trump is the pioneer of a new authoritarian and chauvinist international movement. He is also a warning for us," German Vice Chancellor Sigmar Gabriel said in an interview with the Funke newspaper group.
U.S. neighbor Mexico was pitched into deep uncertainty by the victory for Trump, who has often accused it of stealing U.S. jobs and sending criminals across the U.S. border.
Trump campaigned on a pledge to take the country on a more isolationist, protectionist "America First" path.
He wants to rewrite international trade deals to reduce trade deficits and has taken positions that raise the possibility of damaging relations with America's most trusted allies in Europe, Asia and the Middle East.
(Reporting by Steve Holland in New York and John Whitesides in Washington; Writing by John Whitesides, Alistair Bell and Frances Kerry; Additional reporting by Amanda Becker, Emily Stephenson, Alexander Besant and Christopher Kahn in New York, Susan Cornwell in Washington, Letitia Stein in St. Petersburg, Fla., Luciana Lopez in Miami, Colleen Jenkins in Winston-Salem, N.C., Kim Palmer in Ohio, Timothy Mclaughlin in Chicago,; Editing by Howard Goller and Peter Cooney)