* Right-wing parties push ahead in coalition talks
* President concerned about new parties
* New party Public Affairs sees tough talks
(Adds comment by President Klaus, paras 11-14)
By Jana Mlcochova
PRAGUE, May 31 (Reuters) - Czech right-wing parties reached broad agreement on priorities for the next government following a surprisingly strong win in a weekend election, but said building a coalition would require tough negotiations.
The leftist Social Democrats won the most votes in the election, but combined gains by the three centre-right parties, including two new groupings, made it all but impossible for the left to take power.
The election gave the right a strong mandate to carry out reforms to cut the budget deficit from last year's 5.9 percent. Czechs also sent a clear message demanding a cleanup of politics tainted by corruption scandals by voting for the new parties.
The result cheered markets, sending the crown currency 1.5 percent up to 25.5 to the euro by the afternoon.
Leaders of the right-wing Civic Democrats, conservative TOP09, and centrist Public Affairs said they agreed the next cabinet would focus on fiscal, healthcare and pension reforms, law enforcement, corruption and justice, as well as education, environment and farming.
Radek John, leader of the new Public Affairs party which has no track record in national politics, indicated the talks may not be straightforward.
"Today we agreed very well but of course we are aware that there will be much more difficult topics," he said after meeting Petr Necas, 45, head of the Civic Democrats.
"On the top of that, trilateral negotiations will follow, and that will be even more complicated."
He said there was an agreement on cutting debt with measures including job cuts in state bureaucracy.
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Earlier, the other two groups agreed Necas should become coalition prime minister. Public Affairs has yet to back him.
The coalition would have 118 seats in the 200-seat lower house, a stronger majority than any Czech cabinet has had since the country was created in 1993.
CONCERN OVER NEW PARTIES
President Vaclav Klaus, who gives party leaders a mandate to lead talks on forming a new cabinet and who appoints the prime minister, said he would hold off before asking anyone to conduct negotiations on a more official level.
"I will wait for the negotiations and will not make any formal appointments or award a mandate to anyone," Klaus said on the sidelines of a seminar in Prague.
He said he saw the centre-right cabinet as the only option, although he expressed concern in a newspaper interview about their lack of track record and doubts over whether they have enough qualified personnel.
Given the Social Democrats have a slim chance of being able to form a cabinet, allowing them the first chance to do so would make little sense, even if it would be in line with tradition.
TOP09 was formed a year ago, mostly by defectors from the Christian Democrat Party, shortly after a centre-right government collapsed in the middle of the Czech Republic's term as EU president.
It is led by Karel Schwarzenberg, a pipe-smoking 72-year-old aristocrat and former foreign minister who has a high reputation for personal integrity and has not been tainted by graft scandals. Economic affairs in the party are handled by political veteran and former Finance Minister Miroslav Kalousek.
Public Affairs was founded in 2001 but its activities had been largely confined to Prague city politics until this election. (Additional reporting by Roman Gazdik; Writing by Jan Lopatka; editing by Jon Boyle)