MOSCOW, May 12 - Russia on Monday threatened to stop supplying Ukraine with natural gas if Kiev does not pay in advance for June deliveries, adding that further talks on the issue were also contingent on payment, Reuters reported.

Gazprom chief executive Alexei Miller said the state-controlled Russian company will present Ukraine's state energy company Naftogaz with a "preliminary" bill for June on Tuesday, demanding payment by June 2, Russian news agencies reported.

"If Ukraine does not pay for June supplies, Gazprom will, by 10am (0600 GMT) on June 3, inform the Ukrainian side what amount of gas will be supplied in accordance with the pre-payment," Itar-Tass quoted Miller as saying.

He said the amount of gas to be supplied would be zero if no payment is made, the report said.

Gazprom says Ukraine owes it $3.51 billion and has warned in recent weeks that it would demand pre-payment for gas from next month. The Energy Ministry had previously said the deadline for payment was May 31.

President Vladimir Putin, locked in a standoff with the West over Ukraine's future after annexing its Crimea region, warned European gas customers last month that deliveries could be disrupted if Gazprom cut supplies to transit nation Ukraine.

At a meeting with Miller and Energy Minister Alexander Novak, Russian Prime Minister Dmitry Medvedev said Ukraine has money it can use to pay for gas and European nations should press Kiev to pay, Itar-Tass reported.

"We are within our rights to count on our European partners to send a signal to the Ukrainian leadership that they ought to pay their debts," Itar-Tass quoted Medvedev say saying.

Twice in the past decade, price disputes between Moscow and Kiev have led to reduced supplies of Russian gas to European clients via Ukraine, a conduit for about half the gas Europe imports from Russia.

Ukraine wants to change the conditions of a 2009 contract that locked Kiev into buying a set volume, whether it needs it or not, at $485 per 1,000 cubic metres - the highest price paid by any client in Europe.

Putin gave Ukraine a discount last year after then-President Viktor Yanukovich spurned landmark deals with the EU, but Russia jacked up the price again after Yanukovich's turn towards Moscow led to his ouster at the hands of pro-Western protesters.

Russia will be ready to hold more talks with Ukraine on its gas supplies only when Kiev pays off its debt, Russian Deputy Energy Minister Anatoly Yanovsky said earlier on Monday.

"We want contract liabilities to be fulfilled... To continue talks, the debt should be paid," Yanovsky told reporters. (rt/ez)