A day after his government fell in a no-confidence vote, forcing his handpicked prime minister to resign, President Emmanuel Macron of France lashed out at his political opponents on Thursday, calling them irresponsible and power-hungry, and declaring he would not step down.

He also attempted to calm the country and sketch a way out of the chaos created by a deadlocked, angry lower house of Parliament. He promised to appoint a new prime minister in the coming days who could form a government that reflected a broad cross-section of parties, and could pass an emergency budget to avoid a shutdown of essential state services.

“A new era must start, in which everyone must work for France and where new compromises must be built,” Mr. Macron said in a 10-minute televised address from his gilded office in the Élysée Palace. “We can’t afford divisions or inaction.”

It seemed unlikely that the speech would be enough to calm the president’s growing number of detractors.

The country was still reeling from the night before, when a majority of lawmakers voted to topple Prime Minister Michel Barnier and his cabinet less than three months after it was formed. That made it the shortest-tenured in the history of France’s Fifth Republic.

The lawmakers’ move put France’s 2025 budget in limbo, delaying measures needed to address the country’s towering debt and widening deficit.