* Ukraine gas debt to rise to $5.2 bln in June
* Ukraine wants new gas price set
* Moscow has set June 2 deadline for June pre-payment
* Gazprom's CEO hopes for gas agreement within next few days
(Adds Gazprom source, details)
BRUSSELS/ATHENS, May 29 (Reuters) - Talks between Russia, Ukraine and the European Commission to resolve a gas dispute will go ahead on Friday, the Commission said, as time runs out to avert a threat that Moscow could cut off supplies to Ukraine.
Ukraine is also the transit nation for around half of the gas Russia sells to the European Union, so the dispute threatens onward supplies to Europe.
The Commission, the EU executive, has already brokered two rounds of talks in Berlin following Moscow's threat to stop supplying Kiev with gas if it fails to make a pre-payment for June supplies by June 2.
At talks on Monday, Energy Commissioner Guenther Oettinger said the two governments would study his proposal that Ukraine pay off part of the debt Gazprom says it owes.
Ukraine has said the price for 2014 should be agreed first before it starts making any payments. Russia's energy minister has said Moscow and the EU have proposed that Kiev pay Gazprom $2 billion by May 30, and another $500 million before June 7, as a precondition for a price discount and further talks.
A Gazprom source told Reuters on Thursday that the company had not yet received any payments from Ukraine. Gas flows to Europe via Ukraine, however, remained stable.
Gazprom's Chief Executive Officer Alexei Miller struck a note of cautious optimism, saying in Athens that he hoped the agreement with Ukraine would be reached in the next few days, and so avert supply cuts to Europe.
European Commission spokeswoman Sabine Berger said a third round of talks would take place in Berlin on Friday afternoon, and a spokeswoman for the Russian Energy Ministry confirmed that Moscow would take part in the talks.
Gazprom has said Ukraine's debt for gas supplies will have risen to about $5.2 billion by June 7 unless Ukraine begins to pay it off, but Ukraine has countered that Gazprom owes it around $1 billion for gas following Russia's seizure of Crimea.
Oettinger said on Wednesday he was working on getting Russia and Ukraine to agree on "a fair price" over the coming days, but some of the related issues would be too complex for a quick solution.
(Reporting by Barbara Lewis and Harry Papachristou; additinal reporting by Denis Pinchuk in Moscow; Editing by Will Waterman)