A Foreign Ministry statement said on Saturday the offer came in a telephone conversation on Friday between Sergei Lavrov, the Russian foreign minister, and Mahmoud Abbas, the Palestinian president.
"Mahmoud Abbas highly appreciated the intention of Russia, confirmed by Lavrov, to grant the Hamas-led Palestinian Authority urgent financial aid in the nearest time," it said.
Russia is a member of the Quartet of Middle East mediators searching for an end to the Israeli-Palestinian conflict, along with the UN, the EU and the US.
The US and the European Union have halted direct aid to the Palestinian Authority because it has not renounced violence, recognised Israel or agreed to abide by interim peace deals.
US, Israel action
Washington has barred American citizens and organisations from most business dealings with the Palestinian Authority.
Israel has also blocked the transfer of customs and tax receipts.
Larvov had earlier criticised the halting of aid, though he has urged Hamas to meet the demands of international mediators.
He said the only way to make Hamas meet international demands was to work with it, not boycott it.
Haniya is confident the Hamas
government will last
It was wrong to deny aid to the Palestinians "purely because in democratic elections they elected a government made up entirely out of Hamas members ... we are convinced that this approach is mistaken", Larvov was quoted as saying last Tuesday.
Russia is the only major power to have received Hamas on an official visit since its landslide win in Palestinian parliamentary elections in January.
Ismail Haniya, the Palestinian prime minister, said on Friday that the "unholy alliance" led by the US would not bring down the Hamas government.