* Obama under pressure for muscular response to Kremlin
* In Warsaw, he unveils support and training for NATO allies
* White House to review force presence in Europe
* Kremlin says no plan for Putin-Obama meeting this week (Updates with Walesa comment, NATO meeting)
By Roberta Rampton and Marcin Goettig
WARSAW, June 3 (Reuters) - U.S. President Barack Obama promised on Tuesday to beef up military support for eastern European members of the NATO alliance who fear they could be next in the firing line after the Kremlin's intervention in Ukraine.
Under attack from critics at home who say his leadership on the world stage has not been muscular enough, Obama unveiled plans to spend up to $1 billion in supporting and training the armed forces of NATO states on Russia's borders.
The White House also said it would review permanent troop deployments in Europe in the light of the Ukraine crisis -- though that fell short of a firm commitment to put troops on the ground that Poland and some of its neighbours had sought.
Stationing troops permanently in eastern Europe would be tricky: many NATO members in Western Europe would baulk at the cost, and a big increase in U.S. forces could prompt reciprocal steps by Moscow and spiral into an arms race.
Moments after landing at Warsaw's Okecie airport at the start of a four-day visit to Europe, Obama set the tone by striding into an aircraft hangar to inspect U.S. fighter jets in Poland for a joint programme with the Polish air force.
"We need to make sure that the collective defense ... is robust, it is ready, it is properly equipped," Obama later told a joint news conference with Polish President Bronislaw Komorowski in Warsaw at the start of a four-day visit to Europe.
"The United States is proud to bear its share of the defense of the transatlantic alliance," he said after their talks in Warsaw. "It is the cornerstone of our security."
As they met, fighting raged in eastern Ukraine for a second straight day as Kiev's army pressed an offensive against pro-Russian separatists holding the city of Slaviansk and said it had inflicted losses on the rebels.
Obama was to meet Ukraine's President-elect Petro Poroshenko in Warsaw on Wednesday and will attend celebrations in France with Russian President Vladimir Putin on Friday to mark the 70th anniversary of the World War Two D-Day landings.
The Kremlin said Putin would hold private meetings on the sidelines with German Chancellor Angela Merkel, French President Francois Hollande and British Prime Minister David Cameron, but the Russian leader had no plans to meet Obama.
The U.S. leader said he had no interest in threatening Russia, but that it must respect Ukraine's sovereignty, rein in separatist fighters there, and work together with Poroshenko. If Russia did not, Obama said, more sanctions have been prepared.
"Mr Putin has a choice to make," Obama said. "That's what I will tell him if I see him publicly. That's what I have told him privately."
Obama said he would offer Poroshenko U.S. support for the Ukrainian economy to help ensure it can get through the winter if Moscow turned off gas supplies in a row over payment.
"I want to hear from him (Poroshenko) what he thinks would be most helpful," Obama said. "We're going to spend a lot of time on the economics of Ukraine."
Washington recognised that Russia had a historic relationship with Ukraine and had legitimate interests in what happened along its border, he said.
"But we also believe that the principles of territorial integrity and sovereignty have to be respected," he said. "We have prepared economic costs on Russia that can escalate if in fact we continue to see Russia actively destabilising one of its neighbours in the way that we've seen of late."
While Washington proposed enhancing its military presence on Russia's western border, on another flank it stepped back in the face of a resurgent Kremlin.
U.S. forces ceremonially handed over the Manas air base in former Soviet Kyrgyzstan to the local authorities after using it for years as a key staging post for Western military operations in Afghanistan. The Kyrgyz parliament, seeking to curry favour with Moscow, had ordered Washington to vacate the base.
Poland, which spent much of its history under Russian domination and is now one of the most hawkish NATO members, has previously said it wanted a large U.S. force on its soil as soon as possible.
However, Komorowski said the U.S. pledge on military support was a good response to the security threats in the region since Russia annexed Ukraine's Crimea peninsula earlier this year.
"For us it is most important that ... there are no countries that are told by some outside countries, particularly Russia, whether U.S. forces can or cannot be stationed there," Komorowski said.
The military assistance for Europe proposed by the White House, called the European Reassurance Initiative, is to include greater U.S. participation in training and exercises, deploying U.S. military planners, and more persistent naval deployments in the Black Sea and Baltic Sea, on Russia's doorstep.
The White House said in a statement it would help build the defence capacity of Ukraine and two other Western-leaning states on Russia's borders, Georgia and Moldova. Obama would be seeking the support of the U.S. Congress for the plan, it said.
"In addition to this initiative, we are reviewing our force presence in Europe in the light of the new security challenges on the continent," it said.
At a separate meeting in Brussels of NATO states, U.S Defense Secretary Chuck Hagel urged allies to raise their defence budgets in response to the Ukraine crisis, something several of them are reluctant to do.
Obama's visit to Poland coincides with the "Freedom Day" anniversary, marking the holding of the country's first partially-free elections 25 years ago, which led to the end of communist rule and the victory of the Solidarity trade union.
Lech Walesa, the man who led the Solidarity movement, and was awarded the Nobel Peace Price, accused Washington of failing to show leadership today, echoing some of Obama's critics at home in the Republican Party.
"The world does not have politically moral leadership at the moment," Walesa said in an interview with broadcaster CNN. "The world is a very dangerous place if there is no world leadership... They (the Americans) should finally start acting like a superpower again." (Additional reporting by Lesley Wroughton and Jakub Iglewski in WARSAW and Adrian Croft in BRUSSELS; Writing by Jeff Mason and Christian Lowe; Editing by Paul Taylor and Anna Willard)