Chancellor Angela Merkel's conservatives and the centre-left Social Democrats have embarked on a final push for an agreement on a new German government, though negotiators appeared likely to need one more day.

The effort to put together a governing coalition is already post-Second World War Germany's longest and will not finish with these talks.

A deal will require approval in a ballot of the Social Democrats' members, many of whom are sceptical about renewing the alliance that has governed Germany since 2013 after a disastrous election result in September.

Mrs Merkel's Christian Democratic Union, its Bavaria-only sister, the Christian Social Union, and the Social Democrats set Sunday as a deadline to wrap up negotiations, though they have budgeted two extra days as a precaution.

Angela Merkel.

"The three parties have agreed and come closer on many points in recent days, but there are still issues to discuss - particularly on questions of social policy," Social Democrat leader Martin Schulz told reporters as he arrived at the talks.

Those include labour and health policy questions that are a priority for his party.

"I am still interested in making quick progress, but we want to give Germany a stable government, and a stable government involves a durable coalition deal that is agreeable to all," he said. "So, in the end, we must take the time that we need to create such a stable foundation."

Mrs Merkel said "important points" had to be cleared up. "We know what task we have and are trying to do justice to it," she said.

News agency dpa reported later on Sunday, citing unidentified participants, that the negotiations would have to continue on Monday.

Senior Social Democrat lawmaker Hubertus Heil told ARD television that "a few central sticking points" remain. "If we can't do it tonight, we will continue tomorrow, because the problems have to be solved," he said.

Mrs Merkel's attempt to put together a government with two smaller parties collapsed in November.

Mr Schulz, who had previously ruled out renewing the "grand coalition" of Germany's biggest parties, then reversed course but still faces resistance from parts of his party.

Failure to reach an agreement, or a deal's rejection by Social Democrat members, would leave a minority government under Mrs Merkel or a new election as the only viable governing options.