The role of the Czech president is influential; Mr Zeman can name the prime minister and sign bills passed by parliament into law.
He has promised to give Prime Minister Andrej Babis, a billionaire businessman, a second chance to form a government after his minority cabinet lost a confidence vote in parliament last week.
Mr Zeman's current presidency does not end until March, so he plans to reappoint Mr Babis next month.
His position also allows him to appoint central bank board members and judges.
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10:40
Czechs have been going to the polls in a tightly contested presidential election run-off, seen as a vote on the Czech Republic's direction.
The election sees pro-Russia and anti-immigration President Milos Zeman seeking a second five-year term against Jiri Drahos, a pro-EU academic with no previous political experience.
Polls suggest that 10% of voters are still undecided.
Polling stations will reopen for a second day on Saturday.
Voting will end at 13:00GMT, with the result expected a few hours later.
The politically incorrect president dividing a nation
Voting on Friday, Mr Zeman said Mr Drahos lacked experience.
"My opponent is someone who has not yet practised politics," he said.
Meanwhile, Mr Drahos thanked his supporters, saying their "energy will not be thwarted, whatever the outcome", AFP reported.
In the first round, Mr Zeman had 38.6% of the vote while Mr Drahos won 26.6%. Most of the defeated candidates have since endorsed Mr Drahos.
The election has reflected divisions between low-income voters with lower education and those living in rural areas, who tend to vote for Mr Zeman, and wealthier and well-educated residents of bigger cities, who are likely to prefer Mr Drahos, correspondents say.
The post of president is largely ceremonial but hugely influential. It picks, for instance, which politician can form a government.
Mr Zeman has promised to give Prime Minister Andrej Babis, a billionaire businessman, a second chance to form a government after his minority cabinet lost a confidence vote in parliament last week.
Mr Zeman's current presidency does not end until March, so he plans to reappoint Mr Babis next month.
Who's who in Czech run-off?
Milos Zeman, 73
Joined the Communist Party in 1968 during the "Prague Spring" but was expelled in 1970 for opposing Soviet intervention that crushed moves towards liberal reforms- After communism fell he joined the left-leaning Social Democratic party and became leader in 1993
- In 2013 he became the third president of the Czech Republic since it split from Slovakia in 1993
- In his outspoken remarks on immigration he once said that Muslims were "impossible to integrate" into Europe
- In the EU, he has fiercely opposed sanctions against Moscow and has made improving relations with China a priority
Jiri Drahos, 68
- Studied chemistry and technology and was president of the Czech Academy of Sciences from 2009 to 2017
- He is a supporter of EU and Nato membership but opposes the EU's quota system for distributing migrants
- He considers himself a centrist politician who can unite the country
- He has never belonged to any political party, and claims spread on social media that he collaborated with the StB (secret police) were proved false
- After the first round, he told the BBC that he wanted to "end the climate of populism and fear in Czech society" that has marked Mr Zeman's presidency
BBC
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