* Two right-wing parties push ahead coalition talks
* President concerned about new parties
* President meets party leaders
By Roman Gazdik
PRAGUE, May 31 (Reuters) - Two Czech right-wing parties agreed on priorities for the next government on Monday, a sign of quick progress in talks to form a three-party centre-right coalition after a weekend election.
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 them to take power.
Leaders of two of the right-wing parties, Civic Democrats and TOP09, agreed on Monday on policy priorities, but negotiations with the third party, Public Affairs, were expected to be tougher.
Last week's election gave the right a strong mandate to carry out fiscal 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 25.47 to the euro in morning trade.
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Petr Necas, leader of the right-wing Civic Democrats, and Karel Schwarzenberg of the conservative TOP09 agreed the next cabinet would focus on fiscal and pension reforms, healthcare, law enforcement, corruption and justice, as well as education, environment and farming.
"We have agreed that we will agree," Schwarzenberg said after the talks.
TOP09 also agreed Necas, a 45-year old leader of the Civic Democrats, should be the prime minister.
TOUGHER TALKS AHEAD
The two parties' agendas are very close and it is expected that the harder part of the coalition talks will be reaching an agreement with the centrist Public Affairs party, a new untested grouping led by a popular former TV presenter.
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.
President Vaclav Klaus expressed concern about 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 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 were largely confined to Prague city politics. [
]Klaus met Social Democrat acting chief Bohuslav Sobotka on Monday, 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 admitted he did not see much 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 Charles Dick)