* Senate panel could vote on legislation next week
* U.S. military tries to reassure U.S. allies in Eastern Europe
* Reid sees "two-step process" of Ukraine aid, Russia sanctions (Recasts; adds details on aid legislation introduced in House)
By Patricia Zengerle and Phil Stewart
WASHINGTON, March 5 (Reuters) - U.S. lawmakers could vote within days on legislation to aid the government of Ukraine as it seeks to rebuild the country and struggles to halt Russian military incursions, but they are still undecided as to how Washington should best deal with Moscow.
Republican leaders in the House of Representatives made a rare show of support for President Barack Obama earlier on Wednesday, saying they would work with the White House to address the crisis in Ukraine.
Majority Leader Eric Cantor said the House would soon consider a $1 billion loan guarantee package for Ukraine, which the administration has called for, and look at measures to "put significant pressure on Russia to stop the flagrant aggression to its neighbor."
"The world community should stand united against this invasion, America should be leading and we'll vote soon on legislation to aid the Ukrainian people," he told reporters.
House Speaker John Boehner, who has had frosty relations with Obama, said the House would work in a bipartisan way with the Democratic president, who spoke with British Prime Minister David Cameron as part of intensive international diplomacy.
Later in the day, leaders of the House Appropriations Committee said they had introduced legislation to provide loan guarantees to Ukraine. The measure would be financed within the existing State Department budget, so it does not require additional funds.
U.S. senators are preparing their own bill to aid Ukraine. It could be introduced within days, with a vote in the Senate Foreign Relations Committee next week.
Military leaders testified at a Senate hearing that they were boosting training with Poland's air force and providing more U.S. aircraft to a NATO air policing mission in the Baltics, seeking to reassure allies without escalating the Ukrainian crisis.
Lawmakers have not agreed on what steps to take against Russian President Vladimir Putin's government for its actions in Crimea, where Russian forces have seized control, and to discourage Moscow from further interference in its western neighbor.
U.S. Secretary of State John Kerry was in Paris for talks aimed at easing tensions and averting the risk of war, as the European Union offered the new Kiev government 11 billion euros ($15.1 billion) in financial aid over the next few years.
Majority Leader Harry Reid, who leads the Democrats in the Senate, said he expected there would be a two-step legislative process on Ukraine - first a bill to extend aid to Kiev and later to approve sanctions on Russia.
TARGETING OLIGARCHS NOT SO SIMPLE
Some members of Congress have suggested halting visas and freezing the assets of Putin and those in the Russian elite close to him who are considered responsible for the actions in Ukraine.
Others have advocated sanctioning Russian banks, kicking Russia out of the Group of Eight major industrialized nations or cutting back on U.S. trade with Russia.
"The oligarchs around Putin have a tremendous amount of money in Western banks," U.S. Representative Ed Royce, the chairman of the House Foreign Affairs Committee, said on MSNBC.
"And, likewise, the state-run banks in Russia, they're involved in a lot of money laundering. And clearly under a sanctions regime, with an investigation by the Treasury Department or European governments, those assets could be frozen," he said.
Royce and Democratic Representative Eliot Engel introduced a non-binding resolution in the House on Wednesday that condemned the violation of Ukrainian sovereignty and called for sanctions on Russian officials, banks and state agencies.
A group of Democrats and Republicans offered a similar measure in the Senate, calling for a withdrawal of Russian troops from Crimea and a negotiated settlement. It also urged the Obama administration and the European Union to use "a range of economic and diplomatic leverage" against Russia.
Agreeing on binding sanctions legislation will not be easy. Many lawmakers - including Reid - have suggested that Washington should wait for European nations, which have far more trade with Russia and are more wary about restrictions.
It will take time to determine which banks or individuals were involved in Ukraine, and then to identify assets held in the United States or in U.S.-controlled banks.
"You can't just go after Russian oligarchs because they are Russian oligarchs," a Senate aide said.
Republican lawmakers also offered harsh criticism of Obama's foreign policy.
"With regard to Ukraine, the steps that have not been taken over the last three or four years, (by Obama) frankly, allowed Putin to believe that he could do what he's doing without any reaction from us," Boehner said.
($1 = 0.7278 Euro) (Additional reporting by David Alexander, Richard Cowan, David Lawder and Susan Heavey; editing by David Storey and G Crosse)