Ex-Communist Zeman, 68, a Europe-friendly former prime minister, led the pack of nine contenders with almost 25-percent support with more than 93 percent of votes counted Saturday.
That appeared to set him up for a January 25-26 runoff against Schwarzenberg, 75, who scored almost 22-percent support well ahead of former prime minister Jan Fischer with nearly 17 percent and leftist Senator Jiri Dienstbier with 16.5 percent.
"Milos Zeman is the clear favourite for president. He can easily beat Schwarzenberg or Fischer in round two," the Lidove Noviny broadsheet daily said Saturday, the second day of the two-day first-round vote.
With the powers of the Czech president being relatively limited, issues related to the republic's role in the European Union and corruption woes are key in the election.
Both straight-talking leftist Zeman and rightwing conservative Schwarzenberg have a far more friendly approach toward the 27-nation bloc than Klaus.
Their line echoes the attitude of Klaus's predecessor, the late Velvet Revolution icon Vaclav Havel.
"The Czech Republic should take steps towards more solid EU structures including a single European economic policy," Zeman said in a recent interview, endorsing what Klaus has long described as a nightmare.
As prime minister from 1998 to 2002, Zeman was responsible for negotiating the 2004 EU entry of the 10.5-million-strong ex-Communist country.
Pipe-smoking Schwarzenberg, an aristocrat bearing the full name of Karl Johannes Nepomuk Josef Norbert Friedrich Antonius Wratislaw Mena Furst zu Schwarzenberg, has never concealed his sympathies for the European project.
His backers perceive him as experienced and honest.
"He is the least corrupt and the most experienced when it comes to diplomacy and international contacts," said Alena Poulova, a young IT expert voting in Cernosice just outside Prague, referring to the chronic levels of corruption in Czech politics.
"I feel he would be the least likely to steal," Prague senior citizen Alena Zurkova told AFP after casting her ballot for the politician known as "the Prince".
Preliminary turnout figures topped 60 percent on Saturday afternoon.
The most colourful candidate in the vote in all senses was Vladimir Franz, a 53-year-old drama teacher, classical composer and visual artist with tattoos over his entire body.
The self-described citizens' candidate with no political experience, who has named education, tolerance and culture as his priorities, was fifth according to the preliminary results.
Three women and a rightwing senator seemed left in the dust.
The Czech Republic's previous presidents were elected by parliament, which in February 2012 approved a switch to popular universal suffrage to boost the legitimacy of the office.
Complicating matters ahead of the second round, the centre-right government of Prime Minister Petr Necas faces a no-confidence vote on January 17, which it is expected to survive relying on the support of non-aligned lawmakers.
The no-confidence vote was launched by the leftwing opposition against Necas after he endorsed a wide-ranging prisoner amnesty granted by Klaus that freed close to 7,000 of the republic's 23,000 prisoners, including some jailed or on trial in major fraud cases.
The Czech Republic, a NATO and EU member yet to join the eurozone, has been mired in recession for a year, with its central bank predicting moderate 0.2 percent economic growth in 2013. Joblessness stood at 9.4 percent in December.