The leader of France's Socialist party, Olivier Faure, has thrown his hat in the ring to be prime minister, after the left-wing alliance to which he belongs won Sunday's parliamentary election.
He said he was "ready to assume this function", but only as part of "the dialogue with our partners".
The leftist New Popular Front, which also includes Socialists, Greens and Communists, were the surprise winners on Sunday, but they have nowhere near enough seats to form a credible government by themselves.
Victorious MPs from the left-wing alliance arrived in parliament on Tuesday and called on President Emmanuel Macron to nominate a prime minister from their party.
Under French convention, the president names a prime minister from the winning party. However, Sunday's election has left the country in political deadlock, with no obvious route to a government.
The Popular Front won 182 seats, but the Macron alliance was not far behind with 168, while the far-right National Rally have 143, despite being favourites to win.
With three powerful blocs in French politics, none can form an outright majority of 289 in the 577-seat parliament without reaching out to either of the other two.
Without enough support to survive a "censure" vote of no confidence, there is little chance of any of a left-wing government surviving for long on its own.
There has been some concern among centrists inside the Macron alliance that the president has made no public comment since the election result. He is due to fly to Washington on Wednesday morning for a Nato summit, leaving the political deadlock behind.
The Macron camp, as much as the left, believes it can find a way of forming a minority government.
Instead of naming a new prime minister, the president asked outgoing Prime Minister Gabriel Attal to remain in office "for the time being" to ensure the stability of France. Mr Attal had gone to the Élysée Palace to hand in his resignation after Sunday's election defeat, but the president rejected it.
The Socialist leader's decision to put his name forward on Tuesday indicated tensions among the parties of the Popular Front, who had met the night before in a bid to agree a candidate for prime minister.