Jiri Drahos, 68, the former president of the Czech Academy of Sciences, is considered the most serious contender to unseat Zeman.
Zeman and Babis are among the most popular politicians in the country of 10.6 million that is largely eurosceptic and rejects accepting migrants from the Middle East and Africa. The head of state is also an influential opinion maker and represents the country overseas - a role that Zeman has used to beef up relations with China and Russian Federation while devoting less time to the country's western allies.
Zeman leads polls and should pick up a strong vote outside Prague and other cities on Friday and Saturday, but is expected to fall short of winning over 50 percent of the vote and may face a strong challenger in a run-off set for January 26-27.
The first round of direct presidential election in the Czech Republic started at 14:00 on Friday.
In one example in October, then Prime Minister Bohuslav Sobotka accused Zeman of interfering in Czech foreign affairs and contradicting the government when he repeated his stance against European Union sanctions on Russian Federation over the Ukraine crisis while defending Russia's annexation of the Crimean peninsula as irreversible.
President Zeman has become one of the EU's most outspoken opponents of sanctions against Moscow, with his political ally - newly appointed Prime Minister Andrej Babis - echoing his view.
His more liberal rival Jiří Drahoš is staunchly pro-European and has called for Prague to "play a more active role in the EU".
As the results rolled in, analyst Jiri Pehe told AFP that "Zeman will have a huge problem in the second round".
No candidate is expected to take the lion's share of votes today-polling puts Drahos between 22-27% and Zeman 34-42%.
The combined voter support for the three also-rans stood at 28.24 percent.
Horacek tweeted a picture of him hugging Drahos and wished him "a lot of strength for the fight to come".
As he voted in Prague on Friday, Zeman was targeted by a bare-breasted anti-Kremlin protester who called him "Putin's slut", referring to Russia's president. The 73-year-old is also seen as receptive to authoritarian regimes, while becoming one of Russia's most dependable allies in Europe. According to the Czech Statistical Office, the turnout at the voting was about 60 percent.
After casting his ballot in Prague, Lubos Seidl said the election boiled down to "a clash between the people who think the old way and those who think the new way".
Czech presidents have limited executive powers but Zeman, first elected in 2013, and his predecessors have had a strong influence on public debate.
Milos Zeman once said he wanted "death for all abstainers and vegetarians", he has declared war-literally-to journalists and on environmental groups he said he would treat them "in the medieval way: he would burn them, urinate on them and I would throw salt at them".
"In Czech we say that "the fish stinks from the head" and this perfectly sums up Zeman's presidency", he told the BBC.
But things could change dramatically if Drahos wins.
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