Mr Conte met President Sergio Mattarella, who may ask him to form a stronger government. Last week he lost his Senate majority.
But someone else could become Italy’s PM, or a snap election could be called.
The law professor, who has headed two coalition governments since 2018, tendered his resignation to President Mattarella. And now Mr Conte is discussing the political crisis with Senate president Elisabetta Casellati.
Mr Conte survived a vote of confidence in the lower house, the Chamber of Deputies, last week. He then won a Senate vote, but without an absolute majority.
The lack of a majority threatens to stymie government action – hence the political shake-up.
The confidence vote was called after former PM Matteo Renzi pulled his small, liberal Italia Viva party out of the coalition and said he would only return if Mr Conte accepted a list of demands.
He objects to Mr Conte’s plans for spending €209bn (£186bn; $254bn) of EU recovery funds – part of a €750bn EU rescue for the Covid crisis.
Mr Renzi says EU funds should be invested in promising sectors like digital and green technologies, and he does not want technocrats, rather than MPs, deciding on the allocations.
The anti-establishment Five Star Movement (M5S) has said it will “remain at Conte’s side”.
His resignation comes ahead of a vote on judicial reforms later this week that MPs in his coalition warned he would lose.