* Biden says in Kiev that Russia must act to defuse crisis
* Moscow calls expectations of rapid progress "naive"
* Acting Ukraine president demands new offensive
* Effects of sanctions can be minimised - Medvedev
* U.S. Vice President tells Ukraine to tackle corruption
Ukraine's acting president called for a government operation against pro-Russian rebels who have seized control in eastern towns and cities to be relaunched after a local politician from his own party was found dead and bearing signs of torture.
A previous Kiev offensive failed when the separatists took control of army vehicles, but the United States, Russia, Ukraine and the European Union signed an accord in Geneva last week intended to calm the crisis.
Speaking on a visit to Kiev, Biden called on Moscow to pull back troops built up on Ukraine's borders and persuade the separatists to disarm.
"We've heard a lot from Russian officials in the past few days. But now it's time for Russia to stop talking and start acting," he told a news conference. "We will not allow this to become an open-ended process. Time is short in which to make progress."
The United States has repeatedly warned Russia it faces "mounting costs" if it fails to ensure full implementation of the Geneva agreement, which stipulates the rebels must leave government buildings they have occupied in the past two weeks.
But the Russian ambassador to the United Nations, Vitaly Churkin, ruled out rapid progress. "Of course, it would be naive to suppose that all this could happen quickly," Churkin said in an interview on Rossiya-24 television, adding that about 3 million weapons were held illegally in Ukraine by "radicals" including members of a national guard that Kiev is forming.
"How are these radicals, which sometimes declare themselves to be national guards and thus receive official status, to be disarmed?" he asked.
Russia's annexation of Crimea from Ukraine and the eastern rebellion have deepened the worst East-West crisis since the Cold War, and Biden demanded the removal of Russian forces near Ukraine's frontier that Moscow insists are merely on exercises.
"No nation should threaten its neighbours by amassing troops along the border. We call on Russia to pull these forces," Biden said after meeting Ukrainian Prime Minister Arseny Yatseniuk.
HOSTAGES TO POLITICAL GAMES
Moscow denies it is orchestrating the militants, who say they want the chance to join Crimea in becoming part of Russia following the overthrow of Moscow-backed president Viktor Yanukovich after months of street protests in Kiev.
But Washington has said it would decide "in days" on additional sanctions if Russia does not take steps to implement the agreement.
In Moscow, Prime Minister Dmitry Medvedev promised the country could deal with tougher measures if necessary.
"We shan't give up on cooperation with foreign companies, including from Western countries, but we will be ready for unfriendly steps," he told parliament.
"I am sure we can minimise their impact," he said. "We will not allow our citizens to become hostages of political games."
So far the United States and EU have imposed visa bans and asset freezes on only a limited number of Russians over the annexation of Crimea last month.
Ukraine declared an Easter truce last weekend, and its forces appear powerless in any case to tackle the armed rebels.
Acting President Oleksander Turchinov neverthless demanded more action, saying in a statement that "brutally tortured" bodies had been found near the city of Slaviansk, which is in the hands of the militants.
One was that of Volodymyr Rybak, a member of Turchinov's Batkivshchyna party, who had recently been abducted.
"These crimes are being carried out with the full support and indulgence of the Russian Federation," he said. "I call on the security agencies to relaunch and carry out effective anti-terrorist measures, with the aim of protecting Ukrainian citizens living in eastern Ukraine from terrorists."
The chief mediator for Europe's OSCE security body in eastern Ukraine met separatist leaders occupying buildings in the regional capital of Donetsk on Tuesday. He called their talks "constructive" but gave no indication they would leave.
In Brussels, EU diplomats said the bloc was holding off from imposing further sanctions until it sees whether the Geneva deal works.
The EU has been more cautious than the United States in imposing sanctions on Russia, with some member states worried about antagonising a country that supplies a third of Europe's gas.
Both sides stressed on Tuesday they wanted to depend less on the other over energy.
Medvedev said Russia was more interested than ever in diversifying its gas exports and described talk of Europe importing U.S. gas as a substitute as "a bluff".
Putting the counter argument, Britain said leading Western economies had to tackle the issue when the Group of Seven nations meet next month, noting how Russia had cut off supplies to Ukraine during past disputes over prices.
"It can't be right for Russia to hold individual countries to ransom," said Energy Secretary Ed Davey. "There have been at least two, if not three, occasions in recent times when Russia has sought to use its energy superpower status in quite an aggressive manner," he said in comments published by The Times newspaper.
Partly as a result of the Ukraine crisis, the EU is stitching together measures such as raising electricity production from coal and renewables.
Russia's top natural gas producer Gazprom, however, maintained Europe still needed its supplies. According to most scenarios, long-term gas demand would increase in the European market while production there would decline, it said in a statement issued after a board meeting.
Reuters calculations suggest that the EU steps could slash imports from Russia by around 45 billion cubic metres by 2020, worth $18 billion a year, or the equivalent of a quarter of what Russia currently supplies.
During Biden's trip, the United States offered Ukraine a new $50 million aid package to help with economic and political reform. Of this $11.4 million was earmarked for helping with the election to choose a successor to Yanukovich, the White House said in a statement.
While small in relation to Ukraine's huge needs and a $1 billion loan guarantee already signed with Washington, the package serves to show support for the new authorities following the overthrow of the Kremlin-backed Yanukovich in February.
TOUGH WORDS FOR KIEV
Biden also had tough words for Kiev, saying it must deal with the endemic graft that has sapped the economy and public faith in the state. "To be very blunt ... you have to fight the cancer of corruption," he told lawmakers.
Yatseniuk said Russian special forces were operating in eastern Ukraine to undermine the election due on May 25.
"Everything that is now happening in the east and which Russia is supporting is aimed at wrecking the presidential election," he said. "We demand that our Russian neighbours immediately recall their special forces, which are in the east, recall the army from Crimea and turn this shameful page in which Ukrainian territory has been seized by Russian troops."