Mr. Kwasniewski said Friday he wants to keep the current government in office until parliamentary elections expected later this year. He said accepting Mr. Belka's resignation now would create a power vacuum.
Mr. Belka had been widely expected to offer his resignation after parliament on Thursday rejected his request that it dissolve itself and pave the way for new elections.
Marek Belka became prime minister one year ago, promising to serve only one year. His ruling Democratic Left Alliance is deeply unpopular and trails center-right and populist parties in opinion surveys.
Analysts say Mr. Belka may leave the Democratic Left Alliance and join a new centrist party in the future.
Some information for this report provided by AP.