French President Emmanuel Macron has rejected a resignation offer from the prime minister he appointed, saying instead that the government must "stay on task and act", the BBC reported.

The future of France's prime minister came under threat after Macron lost his absolute majority in parliament, forcing the president to enlist the support of his rivals.

He intends to meet with his political opponents for negotiations.

But neither Marine Le Pen's far-right nor Jean-Luc Mélenchon's left-green alliance are keen to work with Macron's centrist government, which is 44 seats shy of a majority and desperately trying to avoid political paralysis.

The Elysee Palace reported that Borne formally offered to resign Tuesday morning, sending a letter to Macron, who rejected the offer.

The French president refused the offer "so that the government can remain on task and act", the Élysée palace said, adding that he would seek "constructive solutions" to ending the deadlock that threatens his agenda during his second term.