Ferenc Gyurcsany asked for the vote to be held on Friday and said he recognised that it would be about the fact he lied as well as his government's policies.
"I hear the voice of criticism, and I understand the government's responsibility," Gyurcsany said. "Besides the government's policies, this vote of confidence is also about the person of the prime minister."
Partial results from the elections showed that Fidesz, the main opposition party, looked set to win in 18 of 19 counties and 15 out of 23 cities, most of which had previously been held by the socialists.
But Gyurcsany said he had the full support of his governing coalition which includes his Socialist party and the Alliance of Free Democrats.
Istvan Hiller, the Socialist party chairman, said: "The current government coalition ... stands by the policy of reforms and by Prime Minister Ferenc Gyurcsany."
The coalition holds 210 seats in the 386-member parliament and the prime minister is expected to win the confidence vote.
Protesters demanded the prime
minister quit after the elections
Viktor Orban, the opposition leader, called the confidence vote a "deceitful and worthless trick", and demanded a vote of no-confidence in parliament, which would force the coalition government to name a new prime ministerial candidate to replace Gyurcsany.
The losses came after two weeks of protests over a recording in which Gyurcsany could be heard admitting that he had lied to win the elections in April.
The comments were made at a Socialist Party meeting and triggered the biggest street protests since the end of communism in 1989.
On the tape Gyurcsany could be heard saying: "We lied in the morning, we lied in the evening about the economy to win in April."
Laszlo Solyom, the Hungarian president, rebuked the prime minister on Sunday when he said that Gyurcsany had used "impermissible means" to hold on to power and that the crisis had to be resolved by parliament.
Solyom said: "Now parliament has the opportunity to act. Parliament decides on the person of the prime minister. Parliament can restore the required social confidence."