German Chancellor Gerhard Schroeder has held his first exploratory talks with rival Angela Merkel aimed at breaking the political deadlock.
Mr Schroeder was buoyed by the SPD's poll comeback
Mrs Merkel's Christian Democrats (CDU) won Sunday's election, but the margin was too slim for them to govern alone.
She said she would hold further talks with Mr Schroeder, but spoke of "clear differences" between her CDU and his Social Democrats (SPD).
The rival leaders are each insisting on leading any future coalition.
Correspondents say a CDU-SPD "grand coalition" is still regarded as a likely outcome to the crisis - but the talks could take weeks.
The party leaders will meet again next Wednesday, Mrs Merkel said.
Speaking after Thursday's talks, SPD chairman Franz Muentefering said his party was keen to have more detailed talks with the CDU, but he stressed again that Mr Schroeder should remain chancellor.
1. Christian Democrats/Christian Social Union (CDU/CSU): 225
2. Social Democrats (SPD): 222
3. Free Democrats (FDP): 61
4. Left Party: 54
5. Greens: 51
The liberal Free Democrats (FDP), who came third, are traditional allies of the conservative CDU, while the Greens governed with the Social Democrats.
Both the FDP and Greens have said they are unlikely to switch allegiances.
Mr Schroeder argues that the conservative bloc is actually made up of two parties - the CDU and its Bavarian sister party, the Christian Social Union (CSU) - and that the Social Democrats are the strongest single party.
They should therefore nominate the next chancellor, he says.
This has angered the conservative camp, which has been accepted as a single bloc for decades and together received more votes than the Social Democrats.
One CDU leader, Friedbert Pflueger, accused the Social Democrats of "putsch-like" behaviour, using the German word for "coup d'etat".
Another, former interior minister Wolfgang Schaeuble, said the Social Democrats were displaying a "lack of democratic culture".
Angela Merkel ruled out a minority government for Germany
The CDU and SPD have been trying to woo smaller potential partners.
But both have ruled out any deal with the new Left party, which was created by disaffected SPD politicians and former East German communists.
Industry bosses have warned that a prolonged deadlock could damage the German economy.
If no deal is reached, another election may have to be held - probably in 2006.
Greens hold firm
On Wednesday, the Social Democrats held talks with their current partners in government, the Greens, over a future coalition.
But the Greens do not like the idea of the Social Democrats enticing the FDP into a coalition.
On Friday, the CDU will meet the Greens for coalition talks.
The co-chairman of the Greens, Reinhard Buetikofer, has said he cannot picture joining a coalition led by Mrs Merkel.
Mr Buetikofer said the Christian Democrats and Free Democrats both appear to be "searching for an auxiliary motor that would help them, with a majority in parliament, find a way into the chancellery for policies that did not win a majority from voters".
"We are not going to provide this back door," he said.