The leftist Social Democrats (CSSD) won the most votes in the election, but combined gains by three centre-right parties, including two new ones, made it all but impossible for the left to take power.
Klaus separately met all party leaders on Monday including Bohuslav Sobotka, the Social Democrat acting chief, and he may later ask Sobotka 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.
"The CSSD proposes that its representative should be authorised to lead talks on a potential government, in line with the election result and constitutional practice," Sobotka said after meeting Klaus.
Meanwhile, the centre-right parties - Civic Democrats (ODS), TOP 09 and Public Affairs - were in talks on forming a coalition, with a comfortable 118-seat majority in the 200-seat parliament.
Prime minister pick
ODS and TOP 09 have agreed that Petr Necas, 45, chief of the Civic Democrats, should become coalition prime minister.
However, Public Affairs has yet to back him.
The election gave the right a strong mandate to carry out reforms to cut the budget deficit from last year's 5.9 per cent.
Leaders of the three groups 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, 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.
John said there was an agreement on cutting debt with measures including job cuts in state bureaucracy.
Czech debt is one of the lowest among the 27 European Union states, standing at 35.4 per cent of gross domestic product (GDP) in 2009, but it was growing fast on a government deficit of 5.9 per cent of GDP in that year.
In its latest forecast, the Czech National Bank predicted 1.4 per cent GDP growth for this year following a 4.2 per cent slump in 2009, but warned the debt would keep growing to 39.6 per cent of GDP this year and to 43.4 per cent in 2011 if no belt-tightening was carried out.
However, Klaus 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 Lidove Noviny, a daily newspaper, in an interview.
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 72-year-old aristocrat and former foreign minister who has a high reputation for personal integrity and has not been tainted by any corruption scandals.
Public Affairs was founded in 2001 but its activities had been largely confined to Prague city politics until this election.
The new government will replace a non-partisan caretaker team that has been running the Czech Republic since the toppling of an ODS-led centre-right coalition midway through the Czech presidency of the European Union.