* Medvedev calls on EU to help find Ukraine money
* Says he has doubts Ukraine can pay for gas
* EU says there must be no more gas cut-offs
(Adds failure of Russia-Ukraine talks)
By Conor Sweeney and Oleg Shchedrov
KHABAROVSK, Russia, May 22 (Reuters) - Russian President Dmitry Medvedev challenged EU leaders at a summit on Friday to help Ukraine pay its gas bills in order to prevent disruption of Russian supplies to Europe.
The EU and Russia say they want to build relations after a year dominated by rows. But their summit was overshadowed by bickering on energy supplies, trade and Moscow's worries about an EU drive to build ties with former Soviet states.
Failure by Kiev to pay for its gas could threaten a repeat of a dispute in January that left European Union consumers cut off in midwinter from the Russian gas that normally flows to them through Ukraine.
"We have doubts about Ukraine's ability to pay," Medvedev told a news conference with EU leaders in the city of Khabarovsk, a city 8,000 km (5,000 miles) east of Brussels.
"Let us help syndicate the corresponding money for the Ukrainian state. But this should not be only Russia doing this. At the end of the day, it is not us who have problems with paying," Medvedev said.
"We are ready to help the Ukrainian state but we would like a significant part of that work to be perhaps taken on by the European Union," said Medvedev.
European Commission President Jose Manuel Barroso said that confidence could be restored but said there should be no more disruption to gas supplies from Russia, which provides more than a quarter of the 27-member bloc's needs.
"Disruption in the export and transport of gas must not be allowed to occur again," Barroso told reporters. "We ask Russia and Ukraine to do everything in their power to prevent another crisis next year."
When asked by a reporter to give assurances there would be no repeat of the Ukraine gas crisis, Medvedev said: "Russia has given no assurances and will give none. What for?"
The winter dispute with Ukraine raised concerns about
Europe's reliance on Russia's Gazprom
Russian Prime Minister Vladimir Putin and his Ukrainian counterpart, Yulia Tymoshenko, failed to reach a deal on Friday in the Kazakh capital Astana on how to store the gas needed to ensure supplies to Europe this winter.
EASTERN PARTNERSHIP, WTO
Some EU members had hoped for a new start to relations after Putin stepped down as Russian president last year, but a growing list of grievances remain.
European External Relations Commissioner Benita Ferrero-Waldner accepted that relations had been damaged by last year's war between Russia and Georgia, and by the Ukrainian gas dispute.
"There was indeed a rough patch in our relations," she told Reuters, adding that Russia and the EU were now on better terms, a view echoed by Russian officials.
"The mood in the room was not bad," one European official said of the talks, which included Czech President Vaclav Klaus.
EU leaders, however, struggled to convince Medvedev that their new Eastern Partnership initiative to improve ties with Belarus, Ukraine, Moldova, Georgia, Armenia and Azerbaijan was not intended to turn the six former Soviet states against Moscow.
"What we don't want is the Eastern partnership to be turned into a partnership that is against Russia," Medvedev said.
Trade was high on the agenda and a Kremlin foreign policy adviser warned Russia was losing patience over its bid to join the World Trade Organisation after more than a decade of attempts to join the 153-member body.
The European Union's trade commissioner ruled out finalising a strategic pact with Russia before it joins the WTO, and warned Moscow against introducing protectionist measures.
"WTO accession paves the way to the broader free trade agreement we need," Catherine Ashton told Reuters.
"Russia needs to demonstrate it really is keen to move to WTO accession and part of that is not imposing any new duties, which in any event damage business," she said in an interview.
The strategic deal, intended to replace a 1994 pact, makes trade a cornerstone of ties and is still under negotiation. (Additional reporting by Gleb Bryanski in Astana; Writing by Guy Faulconbridge; editing by Mark Trevelyan)