The outgoing technocrat cabinet of Jiri Rusnok was appointed by his leftist ally President Milos Zeman on July 10 after the previous centre-right government fell over a spy and bribery scandal.
Zeman said after accepting the resignation that the cabinet would stay on until a new one can be appointed, "hopefully a cabinet that will emerge from free elections".
The president had signalled on Saturday that he was in favour of snap elections, saying: "I have no reason to unnecessarily put off the declaration on the dissolution of parliament."
Under the constitution, parliament can only be dissolved with the president's consent, and he must set an election date to follow within 60 days.
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The political crisis erupted in June when Petr Necas, the prime minister then, stepped down after his lover and chief-of-staff Jana Nagyova was arrested and charged with bribery and abuse of power.
To fill the vacuum, Zeman named the cabinet led by Rusnok, snubbing rivals from parties in Necas's coalition government.
Analysts say the current political crisis has had little impact on the economy, which the Czech central bank expects to shrink by 1.5 per cent this year.