Hours after quitting, Lecornu accepted a request from French President Emmanuel Macron to work on a plan for the "stability for the country" by Wednesday evening, BBC reported.
That unexpected twist capped a day of political upheaval which saw stocks fall sharply on the Paris exchange amid concerns over the political parties' ability to tackle the country's economic woes.
Lecornu's shock resignation on Monday morning came the day after he unveiled his cabinet, and made him the third French PM to leave office since last December.
His ministerial line-up had been fiercely criticised across the board by parties in the National Assembly, which threatened to vote it down.
The nomination of former finance minister Bruno Le Maire as minister of the armed forces in particular seemed to be a sticking point for many political factions.
On Monday afternoon Le Maire said he was withdrawing from cabinet in a bid to end the crisis.
Shortly after the Elysee Palace announced Lecornu had been given another 48 hours to work out whether negotiations with political parties could result in a "stability plan" for France.
Lecornu was only appointed in September after François Bayrou's government collapsed when MPs refused to back his budget.
MNA
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