* Russia has set Tuesday deadline for payment
* Gazprom says Kiev owes more than $4 billion
* Ukraine, Russian presidents met last week (Updates with start of talks, Oettinger comment, adds PIX)
By Barbara Lewis and Martin Santa
BRUSSELS, June 9 (Reuters) - Officials from Ukraine and Russia met late on Monday in last-minute talks brokered by the European Union to resolve a dispute that could halt the flow of gas from Russia.
After popular protests toppled a pro-Moscow Ukrainian president in February, Russia raised the price it charges Ukraine for gas and has threatened to cut off supplies on Tuesday if Kiev does not pay its overdue bills. Moscow has also annexed Crimea from Ukraine, while armed pro-Russian separatists have tried to split off some eastern parts of the country.
Monday's talks follow a tentative rapprochement last week when newly installed Ukrainian President Petro Poroshenko and Russia's Vladimir Putin met in France at commemorations of the World War Two D-Day landings.
The Commission, the EU executive, announced at the weekend that Russian Energy Minister Alexander Novak, Ukrainian Energy Minister Yuri Prodan and the CEOs of Russian gas producer Gazprom and Ukraine's Naftogaz would attend talks in Brussels, brokered by EU Energy Commissioner Guenther Oettinger.
The negotiations, which began shortly after 7 p.m. (1700 GMT) on a public holiday in much of Europe, follow four previous rounds of trilateral talks as well as bilateral conversations between the two CEOs.
Arriving for the meeting, Oettinger told reporters the CEOs had contacted him at the weekend and asked for trilateral talks to resume as soon as possible.
Separately on Monday, Ukraine said it had reached a "mutual understanding" with Moscow on parts of a plan proposed by Poroshenko for ending the conflict with the rebels in the east.
UKRAINE, EU BOTH AT RISK
The European Union gets roughly a third of its gas imports from Russia, and almost half of that is sent via Ukraine, so if Gazprom cuts off gas to Ukraine, the EU could also face supply disruption.
All sides are anxious for a compromise, analysts say, even if Monday's talks stop short of solving all the issues.
"It is clear that the Russians really want a resolution without a crisis," said Jonathan Stern, chairman of the Natural Gas Research Programme at the Oxford Institute for Energy Studies.
If EU officials could persuade Kiev to use some of the billions of international aid money provided by the EU, the IMF and the United States to at least partly reduce its debt to Moscow, Stern predicted talks could continue and the immediate threat of a cut-off would pass.
Russia gave Ukraine an extra week to clear its debts after it paid a first instalment of $786 million a week ago.
Kiev says it cannot afford the amount now demanded by Russia and wants to pay the lower price that it negotiated in the past.
Details of the price negotiations are a closely guarded commercial secret. Oettinger has said only that the price being considered was less than the $485 per 1,000 cubic metres Russia has demanded and more than the $268.50 Kiev is seeking.
While the dispute has gone on, Gazprom has continued billing Kiev at the higher rate. It says Ukraine owes it $4.46 billion in unpaid bills and the debt is rising at a rate of more than $1 billion per month.
Attempts to settle the gas row are complicated by Russia's determination to press ahead with its giant South Stream pipeline, which would deliver gas straight to the European Union, bypassing Ukraine.
The European Commission says South Stream breaks EU law on competition and has asked Bulgaria to halt work on its section of the project, prompting Russia on Monday to accuse the EU of imposing "economic sanctions by stealth". (Editing by Will Waterman)