Hours after Christian Wulff resigned, Germany's political parties were already squabbling over who they would - or would not - back as a new president.

The main opposition parties, which Merkel said her coalition would consult with, made clear they would not rubberstamp any candidate the ruling parties mooted.

And they laid down a ground rule: "If we are going to come to an agreement, then it cannot be a member of the cabinet," said top Social Democrat Frank-Walter Steinmeier on Friday evening to television broadcaster ARD. His comments were echoed by Green party whip Jürgen Trittin.

Wulff's successor should "if at all possible, not be an active politician of a party," the leader of the Social Democrats, Sigmar Gabriel, said at a news conference after a meeting with the Greens on Saturday.

Labor Minister Ursula von der Leyen and Finance Minister Wolfgang Schäuble, Merkel's Christian Democratic Party (CDU) colleagues, had come up as possible candidates.

'Not by the grace of the Social Democrats'

Gauck has broad popular appeal

But Volker Kauder, the CDU/CSU parliamentary whip, pointed out the coalition parties have a majority in the Federal Convention, the body that elects the president. There would be no candidate by the "grace of the SPD," he said.

The coalition parties - the CDU, its Bavarian sister party CSU and the Free Democrats (FDP) - have a majority of around four seats in the Federal Convention.

The coalition party leaders met for talks on Saturday morning, though any results were not made public. Media reports said they would likely decide on a candidate to present to the SPD and Greens this weekend.

The SPD, for their part, have again put forward the name of Joachim Gauck, a Protestant pastor and former chief of the Stasi East German secret police files. The Social Democrats and the Greens had backed him in the 2010 presidential election.

Watch video 01:57 Opposition wants hand in picking president

Left want in

The Left party, the third-largest opposition party, insisted they too should be included in the consultations.

"Merkel would be wise to look for a solution together with all of the parties represented in the Bundestag," party chief Klaus Ernst told the Rheinische Post newspaper. Parliamentary Leader Gregor Gysi called it "highly undemocratic."

Merkel had mentioned only the SPD and the Greens when she spoke of finding a candidate the opposition could also get behind.

The Greens co-leader Cem Özdemir on Sunday criticized Merkel for wanting to exclude the Left party, but he also said that the Left party failed to support Gauck last time round.

The Federal Convention must elect a new president by March 18.

Meanwhile, prosecutors launched a criminal investigation into allegations that the former president, Christian Wulff, improperly received and granted favors. Wulff had resigned on Friday after a state prosecutor asked parliament to lift his immunity to allow an investigation. He had been under fire since mid-December.

ncy/ng/ccp (Reuters, AFP, dpa)