Milos Zeman, the incumbent head of state, made the comments during a TV debate with his political rival, pro-EU challenger Jiri Drahos, as they battle a closely contested election-run off.
The decision made by nearly 8.4million Czechs could result in a drastic change for the politics of the country and even its future membership of the EU.
Mr Zeman said Czech citizens should have a direct say on political issues and that he is not opposed to a referendum on EU membership.
The 73-year-old said: “Brexit is a decision that must be respected”
This was in stark contrast to Mr Drahos, who expressed his opposition to allowing the people a referendum on leaving the EU.
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He went as far to say it would be “very dangerous” to allow such a vote and was not even sure ordinary citizens could assess an EU exit well.
Mr Drahos, the former head of the Academy of Sciences, said: “We are not Switzerland, which has a centenary referendum tradition.”
When asked about their views on the euro both politicians were reluctant to reply as to whether there should be a date to introduce the euro in the Czech Republic by the end of the five-year-term.
Mr Zeman declared he was for the adoption of the common currency, in principle, but he did not want to allow “Czech taxpayers to pay Greek debt”.
He said: ”The moment Greece leaves the eurozone or is excluded, I will gladly support it.”
Mr Drahos, 68, was equally weary discussing the euro and said he wants to ”first start a debate on the euro” but with no pressure for a date for the introduction of the currency.
He said trying to do so, in the current situation, would be “suicide” for any government, where the majority of Czechs are opposed to it.
Both candidates expressed their opposition to refugee quotas being imposed on the Czech Republic by the EU.
Opposition to an EU plan to redistribute asylum seekers around the bloc has turned many Czechs against the EU and poll last year showed it was the most eurosceptic nation among all 28 member states.
They both stressed the need to protect the EU’s external border well and to help the refugees in their countries of origin, with Mr Zeman saying that it was also necessary to deport the illegal migrants who had not been granted asylum.
In the first ballot two weeks ago Mr Zeman had scored 38.6 per cent of the vote and was well ahead of Mr Drahos with 26.6 per cent.
It is only the second direct election of the president by the people since a constitutional amendment in 2012.
The polls opened today and will close tomorrow.
Additional reporting by Monika Pallenberg