The NFP - consisting of the hard-left France Unbowed, the Socialists, the Communists and the Greens - has proposed civil servant Lucie Castets as its candidate for prime minister, but is almost 100 seats short of a majority, DPA reported.
Green Party Leader Marine Tondelier called Macron's announcement a disgrace and said he was ignoring the election results. France Unbowed's parliamentary group leader Mathilde Panot even threatened Macron with impeachment proceedings.
Macron argued that a left-wing government would only lead to instability because it would come under intense opposition from other parties and could be toppled in an early no-confidence vote.
"My responsibility is that the country is not blocked nor weakened," Macron said in a statement.
He called on the NFP's Socialists, Greens and Communists to "cooperate with other political forces" in order to form a government. He did not mention France Unbowed, which mainstream parties see as dangerous as the far right.
In fresh bid to end the deadlock, Macron said he will launch a fresh round of talks with the main political parties on Tuesday. He had already met with several parties late last week and on Monday.
Macron's centrist faction, which came in second in the elections, would like to see a sort of grand coalition of more moderate parties.
The president suggested that his talks with various parties on the centre-right and center-left had revealed possible coalition configurations.