* Two main parties agree to hold early election
* No deal on new cabinet
* Working groups to be formed to fight economic downturn
(Adds PM comments, background)
By Jan Lopatka
PRAGUE, March 28 (Reuters) - Leaders of the two biggest political parties agreed the Czech Republic should hold an early election, a first step to overcoming a political crisis brought on by a no-confidence vote in the government.
The political turmoil has undermined the country's position as the current holder of the rotating EU presidency, strengthened the role of eurosceptic President Vaclav Klaus and and raised doubts about ratification of the EU's Lisbon treaty.
News agency CTK quoted leftist opposition Social Democrat leader Jiri Paroubek as saying he had agreed with outgoing Prime Minister Mirek Topolanek on holding an election in October, and on forming working groups to draft measures to fight an economic downturn.
But a spokeswoman for Topolanek said the date had not been determined.
"There was an agreement on holding early election, but not on a date yet," spokeswoman Jana Bartosova said.
Paroubek was not immediately available for comment.
An early election has crystallised as the way out of a political stalemate following the fall of Topolanek's minority cabinet on Tuesday, triggered by defectors from the government camp who joined an opposition no-confidence motion.
No group or coalition has majority in the lower house, and the balance of power is held by a group of independent deputies.
Topolanek's right-wing Civic Democrats and the Social Democrats could agree by law to set an election date prior to the end of the regular term in mid-2010.
The Civic Democrats, gradually catching up with the opposition in opinion polls since Topolanek took the EU presidency, want election as soon as possible, from June on.
The Social Democrats prefer a later date, because they want the effect of the presidency to wane after it ends in June. They also expect more economic gloom could raise their chances, political analysts said.
NO DEAL ON NEW CABINET
Topolanek's team will stay in power until a new cabinet is appointed, or possibly until the polls. It remained unclear who would form a new cabinet.
Topolanek has said he should lead the next administration.
The Social Democrats have called for his cabinet to remain in office until the handover of the EU presidency to Sweden, and then for a government of non-party experts to be formed.
But President Klaus, a political foe of both Topolanek and Paroubek, has said a new cabinet must be appointed quickly.
The government collapse weakened the Czech EU presidency at a time when the EU is preparing for the G20 summit on the global economic crisis and an EU summit with U.S. President Barack Obama in Prague on April 5.
The turmoil has thrown in doubt ratification of the EU's Lisbon treaty, meant to streamline the bloc's decision-making, in the Czech upper house of parliament.
"Europe was right to be alarmed, this can mean a complication," Topolanek told daily Mlada fronta Dnes.
Czech Foreign Minister Karel Schwarzenberg said on Saturday failure to ratify could hurt EU enlargement. [
]. (Editing by Angus MacSwan)