(Adds comment from Dayton mayor, Obama)
By Roberta Rampton and Jeff Mason
WASHINGTON, Aug 5 (Reuters) - After back-to-back mass shootings in two states over the weekend spurred widespread condemnation of his rhetoric and style, President Donald Trump chose to suppress his instinct to attack his rivals - at least for now.
Trump has spent a large part of the summer engaged in attacks on four minority congresswomen and an African-American lawmaker from Baltimore. He has long railed against illegal immigrants, characterizing a surge of asylum seekers from Central America as an "invasion."
That rhetoric and his hard-line immigration policies have exposed Trump to sharp criticism since a lone gunman, who law enforcement authorities say apparently was driven by racial hatred, killed 22 people in a Walmart store in El Paso, a Texas city that sits on the border with Mexico, on Saturday.
A person regularly in contact with Trump and the White House said the Republican president understood that some of his rhetoric may have gone too far and could jeopardize his chances for re-election in November 2020.
"He recognizes that, in a lot of ways, he is playing with fire and walking a tightrope," the source said.
Trump addressed the issue from the White House on Monday, discussing the shooting in El Paso and the weekend's other massacre, in Dayton, Ohio. He tried to focus on empathy for the victims and condemnation of the killers, bigotry, racism and white supremacy.
He did not engage, at least in his official remarks, with Democrats and others who have linked the violence to his inflammatory tweets and comments widely criticized as racist.
That is a departure for Trump, who usually fights back against any criticism, going on Twitter or using the stage at frequent rallies to issue verbal tirades and employ caustic language against his rivals.
Advisers said the tone and formal staging for Trump's remarks on Monday were designed to demonstrate leadership during a difficult time.
"There is a renewed desire by many people to show him being presidential," a second source close to the White House said. "When you have a national tragedy, that's what the country wants. They don't want vitriol, they don't want rhetoric, they don't want verbose propaganda."
Dayton, Ohio, Mayor Nan Whaley, a Democrat, said on Tuesday that Trump's rhetoric "has been painful for many in our community," and the leading Democratic candidates vying to run against Trump in the November 2020 presidential election have blamed him for stoking racial tensions in America.
Democrat Barack Obama, the first black U.S. president, on Monday called on Americans to reject "language coming out of the mouths of any of our leaders that feeds a climate of fear and hatred or normalizes racist sentiments."
Trump responded on Tuesday by referring to a view expressed on a Fox News television show that Obama's comments were unfair because he too faced mass shootings during his presidency and was not criticized by his predecessor, Republican George W. Bush.
Obama has generally sought to keep a low profile since leaving the White House in 2017.
Before becoming president, Trump was a leading voice in a movement that falsely cast doubt on whether Obama was born in the United States and therefore eligible to be president.
The man charged with the attack in El Paso has been linked to a racist, anti-immigrant manifesto posted online, and the murders are being investigated as hate crimes. Eight of those killed were Mexican citizens.
RESTRAINT, BUT WILL IT LAST?
Aside from one tweet on Monday morning blaming news media for "contributing greatly to the anger and rage" in America, Trump was more restrained than usual.
He initially told advisers he wanted to deliver his White House speech from the Rose Garden, but then opted for the Diplomatic Room, condemning racism and white supremacy while standing beneath a portrait of the country's first president, George Washington.
It was the same setting for speeches he had delivered in the wake of mass shootings at a Las Vegas concert, a Florida high school, and a Virginia baseball practice where his friend, House of Representatives Republican Whip Steve Scalise was injured. A senior administration official said Trump wanted to deliver a "somber" speech and show he would take action.
But he stayed away from proposing any sweeping changes to gun laws, and gave no details of how he would deliver on his list of ideas: more resources to address hate crimes, reforming mental health laws, working with social media companies on tools to detect potential mass shooters, addressing video game violence, and keeping guns away from people known to pose a risk of violence.
Critics quickly accused him of ignoring the issue of gun control, and repeated the allegation that he was at least partly to blame for the El Paso attack.
Trump was also panned for a gaffe near the end of his speech when he said, "May God bless the memory of those who perished in Toledo." The shooting was in Dayton. The city of Toledo is in a different part of Ohio.
Defending Trump, White House adviser Kellyanne Conway said Democrats had gone over the top with criticism after the shootings and that he had "put politics and partisanship aside."
Trump has a history of making inflammatory remarks, briefly backing down, and then making them again. Some Republicans said that tendency - if it occurs with regard to the shootings - could hurt him in 2020.
"That's an issue," said Republican strategist Charlie Black, adding that Trump needs to continue with his new message. "We'll see what he does and if he sticks to it."
At some point, Trump probably will defend himself against critics, said Chris Barron, a Republican strategist and Trump loyalist.
"The president does punch back, and I think that it is highly unlikely that he's simply going to take incoming from his political rivals who again view this tragedy as a club by which to beat the president about the head," Barron said. (Reporting by Jeff Mason and Roberta Rampton Additional reporting by James Oliphant and Ginger Gibson Editing by Kieran Murray, Leslie Adler and Jonathan Oatis)
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