Hungarian President Laszlo Solyom has strongly criticised PM Ferenc Gyurcsany over his taped admission that he lied about the economy to win re-election.
The PM is accused of undermining confidence in democracy
He spoke as the centre-right opposition made sweeping gains in local elections, capturing many cities and councils.
The opposition had said Sunday's vote should be a referendum on the prime minister's leadership.
But as results came in, Mr Gyurcsany refused to resign, vowing to press on with his programme of reforms.
"We are continuing with our policies, as am I personally," he told a news conference.
Earlier, President Solyom accused the prime minister of undermining confidence in democracy and using improper methods to keep power.
"The prime minister refuses to admit that he used inadmissible means to keep power," Mr Solyom said.
"The parliament decides who is the prime minister. The parliament can restore society's confidence [in government]. The parliamentary majority holds the key to the solution," he said.
Protesters have been calling for Mr Gyurcsany's resignation
Some analysts have interpreted the president's words as being tantamount to calling on Socialist and Liberal deputies to oust their own prime minister.
The past two weeks have seen daily protests calling for the prime minister to step down.
The government was shaken by a leaked tape in which Mr Gyurcsany is heard saying that the government deliberately misled the public about the state of the economy to help it gain re-election in April.
In Sunday's election the opposition centre-right party, Fidesz, won 18 out of 19 counties and 19 out of 23 cities - but failed to secure the capital, Budapest.
The National Election Office said turnout was 53% - Hungary's highest for local elections since the former Communist country returned to democracy in 1990.
Fidesz has said the government should resign if it does badly in the polls.
The government says that as a local vote, the result will not affect its leadership of the country.
After polls closed, some opposition supporters headed for central Budapest, where the latest demonstration against the prime minister was held in front of the Hungarian parliament.
Drastic reforms of health care, state administration, higher education and energy prices have been announced by the government since its re-election.
More than eight million people were entitled to vote in the municipal elections and were choosing mayors and councillors at local and district level.