Czech Prime Minister Andrej Babis said on Friday he would "never resign", dismissing critics demanding he quit amid accusations he was hindering a fraud investigation.

A coalition partner has been weighing whether to leave the cabinet after Babis' adult son was recorded saying his father wanted him to hide last year to avoid police questioning.

Thousands of Czechs protested against Babis in Prague on Thursday evening.

"I will never resign, never," Babis said on his Facebook page on Friday. "Let everybody remember that: Never."

Opposition parties have called a vote of no confidence in Babis's cabinet, which is expected to be held next Friday.

The centre-left Social Democrats, who are a government partner of Babis's ANO party, are considering whether to withdraw support from the cabinet, although a party source said a number of the party's members of parliament were leaning toward staying.

Babis won support from President Milos Zeman who said late on Thursday he expected the situation to calm down. He said in a television interview he would give Babis another chance to form a cabinet if the confidence vote forced him to resign.

Police charged Babis and two of his adult children last year with fraud, saying they manipulated ownership of one of Babis's firms a decade ago so it would qualify for a €2 million public aid.

Babis is a billionaire businessman and the most popular politician in the country, which is an EU and NATO member. He denies any wrongdoing. He has also dismissed the report about his son that was published by news website Seznam.cz.

Babis's son Andrej told the website's reporters who tracked him to his current home in Switzerland that his father had wanted him to hide last year.