Germany's Greens and business-friendly Free Democrats (FDP) have agreed to begin three-way talks on Thursday with the center-left Social Democrats (SPD) on forming a new coalition government following a national election late last month.

The talks will take Germany a step closer towards a so-called "traffic light" coalition, named for the three parties' colors, following the Sept. 26 election in which no party won an overall majority but the SPD narrowly beat outgoing Chancellor Angela Merkel's conservatives for first place.

The election's close result has kicked off a round of coalition talks with both the SPD and the conservatives courting the two smaller parties to try to secure power.

"The Greens have made the proposal to hold a first exploratory discussion with the SPD ... we have accepted the proposal," FDP leader Christian Lindner told reporters, adding that he had contacted SPD chancellor candidate Olaf Scholz. "In coordination with the Greens, I have proposed to Mr. Scholz that we meet tomorrow for such a trilateral meeting, and that will happen," Lindner said.

Both the Greens and FDP kept open the option of pursuing negotiations with the conservatives but said there would be no parallel talks for now. Unlike many other European countries, where the president or monarch invites an individual party leader to try to form a government, in Germany it is up to the parties themselves. That means coalition talks could take months.

After proposing the three-way talks, Greens co-leader Robert Habeck said his party still had considerable differences with both the FDP and the SPD.

"Many things have not yet been discussed," he said.

At stake is the cohesiveness of a new government, its appetite to shape up Europe's largest economy for the digital era, and the extent of Berlin's willingness to engage on foreign issues to the degree that its allies would like.

The Greens and FDP, which are from opposite ends of the political spectrum and at odds on a range of issues, have worked to bridge their differences and the SPD had said on Sunday it was ready to move to three-way coalition talks with them. Merkel, in power since 2005, plans to step down once a new government is formed.