The parties that hold Germany’s balance of power said they would start talks to decide who they want to join in government after the Social Democrats’ narrow election win over Angela Merkel’s ruling conservatives.

The Greens and the liberal Free Democrats have emerged as kingmakers after Sunday’s historic vote, which the SPD, led by Olaf Scholz, won with 25.7 per cent of the vote compared with 24.1 per cent for the Christian Democratic Union and its Bavarian ally, the CSU.

The election heralds weeks of complex political negotiations. Unless they repeat their current “grand coalition”, neither the SPD nor the CDU/CSU can form a majority government without the two smaller parties.

Both Scholz and his CDU/CSU rival Armin Laschet have claimed the right to try to form the next government and run Europe’s largest economy.

The election flips the script for German coalition-building. Usually, the winning party initiates talks with smaller partners.

Scholz said the SPD, Greens and FDP had all increased their share of the vote, meaning they had a “clear mandate” to form a government together.

“We have to make an effort to form a government made up of the parties that won this election — that is the SPD, with a substantial, growing vote, that is the Greens, and that is the FDP,” he told reporters. “We will make every effort to go down this path together.”

But Christian Lindner, the leader of the FDP, said his party must first speak with the Greens, given that this was the source of “the biggest and most substantive differences” in a potential coalition. The parties are far apart on fiscal policy and how to tackle climate change.

“It therefore makes sense to find common ground from these sometimes polarised positions,” he said.

The Greens came third with 14.8 per cent of Sunday’s vote and the Free Democrats came fourth with 11.5 per cent.

“Neither the CDU/CSU nor the SPD stand for a new start . . . That is why it makes sense that our two parties speak to each other first,” Lindner said.

Echoing Lindner’s stance, Green co-party leader Annalena Baerbock said the election result underlined a desire for change. “We have been given a clear mandate by the voters to ensure a new beginning in our country,” she said.

Laschet insisted the SPD had no automatic right to lead talks. “Just because you get 25 per cent, it doesn’t mean you’re entitled to say you’ll be the next chancellor,” Laschet told reporters. “Olaf Scholz and I should feel equally humble [in the face of these results].”

However, the CDU leader denied he had said the CDU/CSU had received a mandate to form a government. “When you land in second place, you are not entitled [to lead coalition negotiations],” he said.

Green party officials agreed they must speak to the FDP first. The CDU is the FDP’s preferred governing partner and some Green officials said they could envision Laschet and the FDP making an enticing offer to move towards a coalition with the conservatives.

But some Greens say they should not seek to team up with a party that most voters see as the loser of the election and should first try to form a coalition with the party that won the most votes.

After holding power through Merkel for 16 years, the CDU and CSU suffered their worst ever national electoral result. Michael Kretschmer, the CDU leader of the state of Saxony, called the election results an “earthquake” that revealed a mood of change against the party.