Nov 28 (Reuters) - Russian state gas producer Gazprom withdrew a threat to reduce gas supplies to Moldova from Monday but said it reserved the right to lower or halt flows in future if Moldova failed to make agreed payments.

Last week, Gazprom accused Ukraine of withholding gas supplies which pass through the country on the way to Moldova - something Kyiv denied - and said it could start reducing those flows from Monday.

In its latest statement, Gazprom said that Moldovan natural gas company Moldovagaz had paid for gas deliveries in November, adding that it had received payment for what it called gas destined for Moldovan customers but which remained in Ukraine.

However, Gazprom accused Moldova of "regular violations" of payment obligations and added: "Gazprom reserves the right to lower or to fully suspend supplies in case of payment violation."

European gas prices rose last week on Gazprom's threat to cut flows to Moldova, as the supply route via Ukraine is the last functioning Russian gas corridor to Europe.

Gas supplies are a constant source of tension between Russia and Moldova. Gazprom says the former Soviet republic owes it about $9 billion, a debt that has accumulated over decades because of non-payments by the breakaway Moldovan region of Transdniestria, where about 1,200 Russian troops are stationed.

Moldova refuses to recognise the debt as its own. Transdniestria currently uses about 40% of the gas imported by the country, but does not pay the Moldovan government for it and refuses to discuss the issue.

Vadim Ceban, head of Moldovagaz, said on Monday that the advance November gas bill had doubled to $42 million - which he said Moldovagaz had paid - amid increased gas demand by Transdniestria.

In a sign that flows were uninterrupted, Gazprom said separately on Monday that it will ship 42.2 million cubic metres of gas to Europe via Ukraine on Monday, only slightly down from Sunday's level of 42.6 mcm. Both figures include flows to Moldova.

Russia used to supply about 40% of Europe's natural gas, mostly through pipelines, but most of those exports have been halted since the war began.

Moldova and Ukraine last week accused Russia of using gas supplies as an instrument of blackmail, an accusation Moscow rejects. (Reporting by Reuters; Editing by Mark Trevelyan and David Evans)