Mirek Topolanek's conservative Civic Democrats won the biggest share of the popular vote in an election at the weekend, but not a majority in the ex-communist nation's first poll since joining the European Union in 2004.
The Civic Democrats and its two smaller potential centrist allies, the Greens and Christian Democrats, will together hold 100 seats in the 200-member lower house - the same as the ruling Social Democrats and the Communists.
Klaus said: "I invited the chairman of the victorious party, Mirek Topolanek, here to authorise him to lead talks on the political scene on forming a new government."
He said he would soon call a session of parliament for the government of Jiri Paroubek, the Social Democrat prime minister, to resign.
Any solution to the deadlock is likely to produce a weak government, unless the two main parties can forge a "grand coalition" - an unlikely outcome given the acrimony between Topolanek and the incumbent prime minister.
Topolanek, a former businessman who campaigned on a promise to cut taxes and implement fiscal reforms, said he would turn to his natural allies in the talks, and that he would update Klaus on the progress of the talks by the middle of next week.
Topolanek said after meeting the president: "I have specific assurances from two political parties, the green party and the Christian Democrats, about talks on a new government."
Paroubek, whose party came second on a platform of higher social spending, has proposed his party go into opposition, and will wait to see the centre-right government's agenda.
But he is expected to keep any conservative-led cabinet on a tight leash, making reforms unlikely.
Record economic growth of 6% annually, low inflation and public debt, as well as a healthy trade surplus have shielded Czech asset prices from repeated emerging markets sell-offs and domestic political turbulence.
But the result dashed investor expectations that a centre-right government ready to push ahead with an overhaul of taxes, pensions and healthcare would emerge from the vote to keep the country on track to adoption of the euro currency in 2010 or a few years later.