Three out of four top leaders of Germany’s Green Party resigned Tuesday amid soul-searching in opposition parties over why they failed to dislodge Chancellor Angela Merkel from power.

Ms. Merkel is biding her time over setting up a new governing coalition, a process that could take two months or more, while the Greens and the Social Democrats (SPD) — her two options for power-sharing — get over their internal recriminations.

Both of the Greens’ two parliamentary leaders, Renate Kuenast and Juergen Trittin, resigned their posts, leaving the 63 deputies who won seats in Sunday’s general election to find new standard-bearers.

One of the Greens’ two paramount leaders, Claudia Roth, also resigned, effective in November. The other main leader, Cem Ozdemir, says he will seek reappointment at a party conference that month.

Ms. Merkel’s centre-right Christian Democratic (CDU/CSU) bloc triumphed in the election and just missed out on an absolute majority, winning 311 out of 630 seats. Senior Greens said they see little or no common ground to help the chancellor govern.

“How could one do anything with Ms. Merkel?” Ms. Kuenast told Phoenix television.

Horst Seehofer, the CSU leader and Bavarian premier, said the former Greens leaders were not people he could deal with.

The SPD, seen as the front-runner to join a Ms. Merkel-led coalition but still locked in infighting, has requested a delay on exploratory talks until after a Friday evening party meeting in Berlin.

A showdown is expected there between a likely majority favouring a so-called grand coalition of Germany’s two biggest parties and a powerful leftist faction favouring a tripartite alliance with the Greens and the hard-left Die Linke, which could muster 319 seats.

SPD leader Sigmar Gabriel is expected to face demands from the critics to hold a vote among all 470,000 card-carrying party members in Germany on whether to enter a Ms. Merkel-led government, a process that could take until the end of the year.

Hilde Mattheis, a leftist SPD deputy, told Phoenix television, “We must involve them.” She said the vast majority of party members in her North Rhine Westphalia region were against joining a grand coalition.

The 192 deputies of the Social Democratic Party (SPD) met for the first time, and were expected to assemble Wednesday to decide who will lead them on the floor of the Bundestag parliament.

Frank-Walter Steinmeier, the incumbent, is seeking re-election in the first test of sentiment in the party since Sunday’s debacle.

Leftists in the party are hostile to Mr. Steinmeier, a centrist who was foreign minister from 2005-09, but it was unclear if there would be an organized protest against his re-election as caucus chief.

Ms. Merkel may need two months or even longer to secure a coalition partner, with long negotiations, a policy contract in exacting detail, and votes by the participating party conferences required.

Volker Kauder was re-elected joint CDU/CSU caucus leader, making him Ms. Merkel’s floor leader in the legislature.

He said a first approach for a coalition would be made to the SPD, adding, “There is no one at the Greens that we can talk to at the moment.” At the tiny Pirate Party, a group seeking internet freedoms which flared up in popularity two years ago but failed to win any seats in parliament, Bernd Schloemer resigned his party leadership. True to Pirate style, he announced this over Twitter: “Bye bye #Pirates.” Parliamentary speaker Norbert Lammert said he expected to summon parliament for a first meeting on October 22. Observers said the re-election of Ms. Merkel of chancellor might not take place for many weeks after that date.

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