Belarus' ministry of energy also issued a letter to the European Commission warning that cuts of more than 15 per cent could lead to it siphoning off gas to European countries.
But Alexei Miller, the chief of Gazprom, said that transit of gas from Russia to European customers has so far continued despite the threat.
Gazprom had warned Belarus previously that it would eventually cut deliveries of gas by 85 per cent if Belarus does not pay off its debt.
In the letter signed off by Semashko, Belarus said it had offered to cover a May gas bill by Wednesday, while demanding that Russia "immediately" pay the government $217m in gas transit fees.
Belarus would then pay Russia $187m by July 5 to cover January-April supplies, the government said in a statement, asking Moscow to refrain from further energy cuts "until mutual obligations are fully implemented".
"Otherwise Gazprom will force the removal of gas from the gas transit system so that the needs of the Belarussian national economy and population can be satisfied," it said.
Gazprom has said Belarus so far owes it $192m in arrears.
Igor Sechin, Russia's deputy in charge of energy, said on Monday that Belarus would have to make a new payment, bringing the total amount to $270m, by Friday.
Analysts warned of "a new gas war" after supplies were cut and said the Kremlin move was aimed at punishing the government of Alexander Lukashenko.
The president of Belarus has recently irritated Moscow by dropping his normally dependable loyalty in favour of a quest for closer ties with the European Union.
Russia supplies a quarter of Europe's gas needs and uses Belarus, which borders EU member Poland, as one of two key transit routes of oil and gas to the continent.
Gazprom said the ban would not affect its European customers because it will channel alternative supplies via another pipeline through Ukraine from where most gas flows into Europe.