Belka has led a caretaker coalition since last May as scandals left Poland's government at a political stalemate, the BBC reported.
Belka had called for early elections to meet his promise of serving as prime minister just one year.
Parliament rejected holding early elections and Belka resigned Friday.
Kwasniewski, however, refused to accept the resignation, which may force Belka to remain in office until this fall, the BBC reported.
Kwasniewski has said repeatedly he wants to avoid a power vacuum when Poland hosts a Council of Europe summit May 16-17 in Warsaw.