The Czech prime minister insists his coalition government will be ready to assume the EU presidency in January despite a regional election defeat.
"I am not capitulating to hopelessness," Mirek Topolanek said, after his right-wing Civic Democrats had lost in all 13 regions contested.
Jiri Paroubek, leader of the opposition left-wing Social Democrats, called for a new government to assume the EU role.
Mr Topolanek faces a confidence vote in the lower house on Wednesday.
The weekend election saw the Social Democrats (CSSD) sweep the Civic Democrats (ODS) out of all their regional strongholds. Mr Topolanek called it "a slap in the face".
Mr Paroubek said "this government is not able to lead this country nor do reasonable work for the Czech Republic in the European Union".
The Czech Republic assumes the six-month EU presidency on 1 January, taking over from France.
Mr Topolanek, speaking on Czech television on Sunday, said "nobody in Europe" would want him not to take up his position as chairman of the European Council - the body of EU government leaders - in January.
Correspondents say the vote reflects public opposition to a planned US missile defence shield. The Social Democrats campaigned against the shield, which would rely on radar stations in the Czech Republic.
The ODS governs nationally with the Christian Democrats (KDU-CSL) and the Greens (SZ). The ruling coalition lacks a clear majority in the lower house.
"This is a very strong warning, I approach it with humility," Mr Topolanek was quoted as saying after the results were announced.
He voiced regret that his party had not run a centrally-organised election campaign.
The opposition also did well in the 27 Senate seats up for election, threatening the conservatives' absolute majority in the upper house. Run-off elections will be held next weekend.
Mr Topolanek, an engineer and former businessman, was appointed as prime minister in August 2006.
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