Belarus confirmed it had sent a letter to the Russian energy company.
In the letter signed off by Semashko, the government said it had offered to cover a May gas bill by Wednesday, while demanding that Russia "immediately" pay Belarus $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.
Relations between Russia and Belarus have soured since they failed to agree unified customs rules and Belarus gave refuge to Kurmanbek Bakiyev, the ousted Kyrgyz president, despite Russia's support for the new Kyrgyz leadership.
Previous pricing disputes with Belarus have led to oil supply cuts, with Poland and Germany being most affected.
A similar standoff halted the much larger Russian gas supplies across Ukraine for almost two weeks in January 2009, leaving many Europeans without fuel during a cold snap.