They also appoint central bankers and judges and are pivotal in forming governments, a process the Czech Republic - a member of both the European Union and North Atlantic Treaty Organisation - is now going through.
Czech presidents have limited executive powers but previous incumbents have exerted strong influence on public opinion.
He has also sought more trade with China and was the only western leader to attend a military parade in Beijing in 2015. Since then, he's been one of most prominent voices in Europe to call for abolition of sanctions against Russian Federation over the annexation of Crimea from Ukraine.
Zeman is expected to win the first round of elections on Friday and Saturday.
"Femen, an worldwide feminist group that originated in Ukraine, said on its website that the woman was Ukrainian citizen Angelina Diash", reported RFERL.
Security personnel also had to help a visibly rattled Zeman, who walks with a cane, to leave the room.
If none of the candidates could win an absolute majority of the vote, the second round will be held two weeks later, on January 26-27. He regularly holds voter meetings with crowds of people in smaller towns.
"It is a clash between... the post-communist part of society represented by Zeman and the other part, say, modern, pro-Western, which simply doesn't want this president any more", he told AFP. Zeman is followed by pro-EU candidate Jiri Drahos, a 68-year-old chemistry professor and former chief of the academy of science, with 25.3 percent of the votes.
Many voters remainied undecided until the last minute, with Prague archivist Marcela Riegerova saying she "ended up tossing a coin to decide between two candidates, and Drahos came out the victor".
Last October, during a press conference, Milos Zeman took to new levels his open hostility towards journalists by holding a replica of an assault rifle with the inscription: "Towards journalists". "The second round will decide and different rules will apply there", CTK news agency quoted him as saying.
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.
Zeman has backed Babis even as the billionaire businessman has struggled to get support from other political parties while he battles police allegations he illegally obtained European Union subsidies a decade ago.
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". His reelection would reflect a eurosceptic stance by most Czechs and the public's rejection of accepting migrants and refugees. Zeman has sharply criticised immigration from Muslim countries and linked it to security threats.
"What I would be afraid of is infiltration by jihadists, and thus a higher number of terrorist attacks in European countries or cities", he said on TV Barrandov.