Slovak Prime Minister Robert Fico has said he is prepared to resign if the president accepts that the coalition government can continue for the rest of its term without early elections.
Mr Fico said he was ready to present a candidate for PM from his party.
It comes amid a political scandal caused by the murder of a journalist.
Jan Kuciak was investigating government corruption when he was killed. His fiancée Martina Kusnirova was also murdered in an attack at their home.