* Russia, Ukraine unable to agree on gas price
* Monday deadline looms for Kiev to pay some debts
* Row clouded by political tensions, conflict (Adds no agreement, talks to continue on Sunday)
By Pavel Polityuk
KIEV, June 14 (Reuters) - Ukraine and Russia failed to end a gas pricing dispute at talks on Saturday but agreed to meet again on Sunday, a day before a Russian deadline for Kiev to pay a $1.95 billion debt or have its gas supplies cut off.
Halting deliveries to Kiev could disrupt the gas flow to the European Union, which receives gas via Ukraine, but the chances of a breakthrough have been hit by tensions over an uprising by pro-Russian separatists in east Ukraine.
The two sides did little other than set out their positions at talks with European Energy Commission Guenther Oettinger in a Kiev hotel before deciding to resume discussions in the morning.
"Each side explained its position today. No solution was found. Therefore, in line with a proposal by Commissioner Oettinger, the talks will continue tomorrow morning," Ukrainian Energy Minister Yuri Prodan told reporters.
Andrei Miller, the chief executive of Russia's top natural gas producer, Gazprom,, said nothing to reporters as he went in and left the talks.
Resolving the long-running dispute and averting a cut in gas supplies could help ease tension over the separatist rising, which Kiev blames on Moscow despite Russian denials that it is arming the rebellion.
Russia had initially rejected the idea of holding another round of talks over the weekend, but agreed in the end to have one more try.
"We are ready to seek compromise, but it is useless to put pressure on us," Sergei Kupriyanov, spokesman for Russian state gas producer Gazprom, said in Moscow.
The dispute is part a broader crisis in which Russia annexed Crimea from Ukraine in March following the overthrow of the country's Moscow-leaning president, and tensions are high following the shooting down of a Ukrainian military transport plane by the rebels in east Ukraine.
Gazprom has said Ukraine should pay at least $1.95 billion - part of its debt for Russian gas supplies - by Monday, or face being switched to a system under which it would receive only gas it pays for in advance, and possible gas supply cuts.
After the failure of several rounds of talks, the last of which were in Brussels this week, Ukraine's government ordered the energy sector, ministers and local authorities to prepare for supply cuts.
Russia initially demanded at the talks that Ukraine should pay $485 per 1,000 cubic metres of gas but then offered to remove the export duty, a move that would cut the price to $385 - around the average amount paid by Russia's European clients.
Ukraine had held out for $268.5 until Friday, when it said it was ready to pay $326 for an interim period of 18 months while a long-term price was worked out.
Russian energy authorities said last week that the price of $385 was final, but Prodan suggested to reporters Ukraine was not ready to go beyond its offer of $326.
Russia has extended its deadline twice in the past few weeks to allow more time to reach a deal but has made clear it will not do so again.
Russia meets about a third of the EU's gas needs, and around half of the gas is delivered via pipelines that go through Ukraine.
Supply cuts would not be a big problem now because it is summer and the EU and Ukraine have enough gas in storage, but the EU suffered serious disruptions in supplies when Russia cut off supplies in a gas war with Kiev in 2009.
(Additonal reporting by Vladimir Soldatkin in Moscow, Writing by Timothy Heritage, editing by David Evans)