Mrs Merkel’s move wrongfooted the SPD, who have made a pledge to legalise gay marriage a central plank of their election manifesto.
Martin Schulz, the SPD leader and Mrs Merkel’s main challenger, tried to regain the initiative by calling for a vote before the end of the current parliament.
“Angela Merkel made a move yesterday and we are taking her at her word,” he said. “The change of heart should be acted on this week.”
There is thought to be a majority of MPs in favour of legalisation in a free vote in the current parliament.
But the CDU downplayed the chances of a swift vote, with the whips’ office saying there was “no need for a rushed decision”.
Mrs Merkel’s move risks upsetting the right-wing of her own party, and in particular its deeply conservative Bavarian sister party, the Christian Social Union.