PARIS — President Macron said Wednesday he will wait for the country’s political parties to build a “Republican” majority at the National Assembly before he can decide on a new prime minister, after no party won a majority in Sunday’s legislative elections.

Mr. Macron’s comment came in a letter published by several French press organizations as political leaders of various parties have been trying to project themselves as the only solution to the current political turmoil after the inconclusive results.

“Nobody has won,” said Mr. Macron in the letter. “No political force has obtained a sufficient majority on its own and the blocs or coalitions that emerge from these elections are all in the minority,” he said.

Mr .Macron asked parties who adhere to “republican institutions, the rule of law, parliamentary norms, a (pro-)European orientation and the defense of French independence” to build a compromise.

“It is in the light of these principles that I will decide on the appointment of the prime minister,” Mr. Macron said. “Until then, the current government will continue to exercise its responsibilities and will be in charge of current affairs.”

A leftist coalition, the New Popular Front, won more seats than other groups, pushing the far-right National Rally into third place. Mr. Macron’s centrist alliance came second.

The outcome has left France with the unprecedented prospect of a hung parliament and political paralysis.

Outside the National Assembly, the leader of the Les Républicains conservatives in the new parliament, Laurent Wauquiez, said Wednesday his party will introduce a no-confidence vote to try to bring down any government that includes a member from the far-left France Unbowed party, which is part of the New Popular Front bloc.

“We won’t let them attain power,” he said.

Many lawmakers of the New Popular Front insist that, as the largest group in parliament, the prime minister should come out of their ranks.

Mr. Macron called the surprise snap election after the anti-immigration National Rally made huge gains in the June 9 European elections — a risky gamble in the hope that French voters would block the far-right party as they always had in the past.