A week after Chancellor Olaf Scholz’s three-party coalition fell apart over next year’s budget, his party and the main opposition, the conservative Christian Democratic Union, have agreed to hold a snap election on Feb. 23.

The agreement, which The New York Times confirmed on Tuesday, comes as all parties have fired up their campaigns for an early election, which will come about seven months before it had been scheduled.

Last week Mr. Scholz fired his finance minister, Christian Lindner, leader of the pro-business Free Democratic Party. The move effectively dissolved the coalition and sent shock waves through Germany.

Mr. Scholz had announced likely elections in March, but the opposition pushed for an earlier date, arguing that the chancellor would be unable to do much between now and then with a minority government and did not have enough passive support in parliament to pass any new laws.

The date for the new election comes as German leaders gird for an intense campaign over how to restart an ailing economy — and prepare for President Donald J. Trump’s second term in office.

On Sunday, during his first televised interview since the end of the coalition, Mr. Scholz said that he intends to campaign for a second term.