“Mr. Drahos said that he would like to meet me face to face,” the president said. “I am happy to oblige him.”
Election officials said voter turnout was 61.9 percent in the preliminary election. Mr. Drahos called on all those “who want a change” to cast ballots in the runoff.
“The final is still ahead of us, and that’s what matters,” Mr. Drahos said.
Mr. Zeman, 73, a former prime minister, was elected in 2013 during the country’s first direct presidential vote.
Vaclav Havel and Vaclav Klaus, the previous two presidents of the country, were elected by Parliament.
Under the Czech Constitution, the president picks the prime minister after a general election, one of the office’s key responsibilities.
The president also appoints members of the Central Bank board and selects Constitutional Court judges with the approval of Parliament’s upper house.
Otherwise, the president has little executive power since the country is run by a government chosen and led by the prime minister.
Mr. Zeman was considered a more pro-European leader than his euroskeptic predecessor, Mr. Klaus, but in recent years he has used every opportunity to attack the European Union. He has proposed a referendum on the country’s membership in the bloc after Britain decided to leave.
He also has become known for strong anti-migrant rhetoric, which won him support from the populist right. He has divided the nation with his pro-Russian stance and his support for closer ties with China.
He was one of the few European leaders to endorse Donald J. Trump’s bid for the White House.
Mr. Drahos, 68, is seen as more Western-oriented and firmly supports the country’s membership in the European Union and NATO.