French Prime Minister Elisabeth Borne resigned after the presidential force lost its majority in Parliament, but President Emmanuel Macron refused to accept her.
This was announced by the Elysee Palace on Tuesday.
According to a statement from the palace, Macron did not accept Bourne's resignation "in order for the government to remain on task."
Emmanuel Macron will hold talks on Tuesday and Wednesday with opposing party leaders to find "possible constructive solutions," the Elysee Palace clarified.
Macron is under pressure to get his rivals' support for his government's reform agenda. Minority governments are rare in France, and Macron's bloc lacks 44 seats for a majority.
France's centrist government is trying to avoid political paralysis after losing its majority, with some commentators warning that France is becoming ungovernable.
Macron will also have to replace three ministers who lost their seats during Sunday's vote.