* Right-wing parties push ahead in coalition talks
* President concerned about new parties, meets party leaders
* New party Public Affairs sees tough talks
(Adds second coalition meeting)
By Roman Gazdik
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.
Markets gave a cheer to the result, sending the crown currency 1.6 percent up to 25.45 to the euro at 1339 GMT.
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.
<^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
For a full menu of stories, click on [
]http://graphics.thomsonreuters.com/RNGS/2010/MAY/CZECH2.jpg
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^>
Leader Radek John of the new Public Affairs party, which has no track record in national politics, gave indications he may live up to a reputation as a tough negotiator.
"Today we agreed very well but of course we are aware that there will be much more difficult topics," he said after meeting Necas. "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.
Earlier, the other two groups agreed that Petr Necas, 45, chief of the Civic Democrats, 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 must ask parties to form a government, expressed concern about the lack of track record of TOP09 and especially Public Affairs.
"With these two parties, we cannot know how they will behave in real politics," he told daily Lidove Noviny in an interview.
"I have no clue how many people they have prepared to take the posts of immense responsibility as members of the cabinet and parliament."
TOP09 was formed a year ago, mostly by defectors from the Christian Democrat Party, shortly after a centre-right cabinet fell in the middle of its 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 any 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.
Klaus separately met all party leaders on Monday including Social Democrat acting chief Bohuslav Sobotka, and he may later ask him to lead coalition talks.
That would be in line with Czech tradition to give the nominal election winner the first chance to form a cabinet. Sobotka has said the tradition should be kept even though he acknowledges he sees little chance of succeeding.
With no realistic prospect of a left-wing government, Klaus may also go straight to Necas and ask him to lead the talks. (Writing by Jan Lopatka; editing by Peter Graff)