* (Adds possible date on trilateral talks, G7 background)
KIEV, June 6 (Reuters) - Ukraine and Russia will restart talks over the weekend aimed at resolving a dispute over gas prices while Kiev is considering paying off its bill for past supply, a Ukrainian government source said on Friday.
With a June 10 deadline for payment issued by the Russians, the aim is to avert a possible cut-off in flows to Ukraine, a move that could also affect gas supplies to Europe.
Russian gas exporter Gazprom says Kiev owes more than $4 billion for gas already delivered and wants prepayment for future supplies.
"The talks will continue on Saturday, Sunday and Monday. We expect to come up with a decision on Tuesday (June 10)," the Ukrainian government source told Reuters, adding that the Ukrainian leadership may agree to pay off its gas debts for 2013.
The two sides differ on how much is owed by Ukrainian state energy company Naftogaz. Ukraine has put its debt for 2013 and 2014 as of April 1 at $2.2 billion. It paid $786 million last week.
Gazprom, which puts the figure at $4.46 billion, declined to comment on Friday.
European Commissioner Guenther Oettinger has acted as mediator in three-way talks between Ukraine, Russia and the EU.
Russia meets about a third of the European Union's gas needs, with almost half of that piped via Ukraine.
At three-way talks in Brussels on Monday, bringing together the Russian and Ukrainian energy ministers and the Commission, Oettinger said the chief executives of Naftogaz and Gazprom had held separate negotiations citing the commercial sensitivity of price discussions.
A European Commission spokeswoman said on Friday there was no decision on when further trilateral talks might be held, but the Commission had suggested June 11 as a possible date.
Gazprom lowered prices for Ukraine to $268.5 per 1,000 cubic metres in January after Ukraine's former pro-Russia President Viktor Yanukovich ditched plans to forge closer ties between Kiev and the EU.
Russia hiked the price to $485 in April after Yanukovich was ousted and a pro-Western government came to power in Kiev. (Reporting by Pavel Polityuk; additional reporting by Barbara Lewis in Brussels; writing by Vladimir Soldatkin; editing by Jason Neely)