Czech Prime Minister Petr Necas has formally handed in his resignation after a bribery and spying scandal that centred on an aide.
President Milos Zeman's approval is needed for the next prime minister but he has difficult relations with the governing coalition.
Czechs are anxious to avoid a damaging period of political paralysis in the, which has been in recession for a year and a half.
"The worst thing to happen to this country would be weeks of agony," said Petr Gazdik, one of the leaders of the TOP09 party, a junior partner in the governing coalition.
Under the constitution, the whole government must now step down along with Mr Necas.
His administration will stay on as caretakers until a new government is in place.
Mr Necas quit after prosecutors charged the director of his office, Jana Nagyova, with illegally ordering agents to spy on people including Mr Necas's wife, according to lawyers for two defendants in the case.
He said he was not aware of any surveillance, but the fallout from his aide's arrest undermined his position.
Ms Nagyova was also charged with bribing members of parliament to drop a rebellion against Mr Necas last year.
After accepting Mr Necas's resignation, the president scheduled a series of talks with political parties for this weekend and next Monday, to try to identify a candidate for prime minister who could win support in the divided parliament.
The outgoing prime minister's Civic Democratic party wants to form a new government, under a different leader, with their two junior partners and see out their regular four-year term that expires next May.
The party's leadership met earlier but it did not reveal who its possible candidate would be.
One choice would be industry minister Martin Kuba. He became the party's acting chairman after Mr Necas quit his other job, as party leader.