US Vice President Joe Biden on Tuesday accused Russia of "trying to pull Ukraine apart" and pledged Washington's strong support for Kiev's leaders, as a Cold War-style confrontation over the former Soviet republic ratcheted up. Biden was speaking in Kiev amid worrying signs on the ground that diplomacy was failing to calm the crisis. Pro-Kremlin rebels in Ukraine's east overnight claimed control of the police station in the town of Kramatorsk, where they already occupied the town hall. Ukraine's acting president, Oleksandr Turchynov, said the new seizure "puts a cross through all the agreements reached in Geneva". That referred to an accord signed last Thursday by Ukraine, Russia, the United States and Europe designed to de-escalate the volatile situation and prevent it spiralling into civil war, or worse. But the pro-Moscow separatists -- who Kiev and Washington say are backed by Russian special forces -- are ignoring the accord's demands that they disarm and cease occupying buildings in a string of eastern towns. Russia says Kiev's leaders -- whom it regards as illegitimate -- are to blame for the collapse of the accord. It says ultra-nationalists involved in months of Kiev protests that ousted pro-Kremlin president Viktor Yanukovych in February killed rebels in an attack Sunday near the eastern town of Slavyansk. A funeral for the militants was held on Tuesday. Bells rung loudly from Slavyansk's Orthodox church and women wept as three coffins were carried out. - Biden urges Russian pullback - Tens of thousands of Russian troops are massed on Ukraine's eastern border in what NATO believes is a state of readiness to invade. The United States and NATO have responded by boosting their own forces in eastern Europe. Biden, after meeting Ukraine's leaders in Kiev, called on Russia to pull back those forces, and to reverse its annexation last month of Ukraine's Crimea peninsula. "We in the United States stand with you and the Ukrainian people," Biden said in a joint news conference with Ukrainian Prime Minister Arseniy Yatsenyuk. Russia, Biden said, faces "more costs and greater isolation" if it keeps fuelling separatist unrest in Ukraine. "There are some who are trying to pull Ukraine apart," he said. Washington has threatened to impose more sanctions on Moscow, on top of travel bans and asset freezes already applied to members of President Vladimir Putin's inner circle. "Time is short to make progress," Biden warned. He added that the United States was stepping up to help Ukraine lessen its dependence on Russian gas, fight corruption, and prepare for a May 25 election to choose a new president. The United States, he said, wants to see Ukraine "hold together as a single state, united and sovereign." But Russian Prime Minister Dmitry Medvedev dismissed the US threat of new sanctions. "I am sure we will be able to minimise their consequences," he said in a televised speech to the Russian parliament. - EU divided on further sanctions - However, even though he insisted his country could function in isolation if necessary, he acknowledged that Russia's economy was facing an "unprecedented challenge". Russia's finance ministry said Monday the energy-rich nation could tip into "technical recession" over the next three months. Finance Minister Anton Siluanov warned last week that Russia was facing the toughest economic conditions since 2009, when it went into a serious slowdown. Faced with a worsening crisis, Washington and Moscow have urged each other to rein in each side in Ukraine and revive the Geneva accord. The European Union, meanwhile, is divided on going further with its own sanctions on Moscow, with some member states worried that increased punishment could jeopardise supplies of Russian gas. As the crisis plays out, the insurgents in Ukraine's east remain firmly entrenched in public buildings they have occupied for more than a week. In the town of Lugansk, close to the Russian border, protesters who have been occupying local security buildings staged a fiery mass demonstration Monday and pledged to hold their own local referendum on autonomy on May 11, the Interfax-Ukraine news agency reported.   Although highly trained military personnel whose camouflage uniforms are stripped of all insignia are helping the rebels secure the some 10 towns they hold, Putin denies they are Russian special forces. However, the US State Department released images Monday that it claimed proves armed separatists in eastern Ukraine are actually Russian military or intelligence officers. The photos, said the State Department, showed a military fighter with a distinctive red beard seen in Georgia in 2008 -- when Russia invaded -- wearing the insignia of a Russian special forces unit. The same man is also pictured in Crimea and Slavyansk. Other images from Slavyansk show men carrying the same kind of RPG-26 rocket launchers as those issued to Russian troops.