The failure of preliminary coalition talks, after weeks-long negotiations, has led to political uncertainty in the EU's largest economy.
"After serious discussions, we agreed that after the collapse of exploratory talks between the conservatives, the Greens and the Free Democrats, the SPD will work constructively to find a way out of this situation", an SPD statement read.
Schulz backed off his flat refusal to consider a renewed "grand coalition" of Germany's two biggest parties, saying in Berlin on Friday that the Social Democrats "won't play an obstructionist role" in parliament.
Schulz has said the election reflects voters' opposition to another coalition between Merkel's conservatives and the SPD.
However, Merkel's talks with two other parties, the left-leaning Greens and pro-business FDP, collapsed early this week when the FDP unilaterally pulled out.
The breakdown of talks has left Merkel with few options left to form a new government after September's election, with some hoping the talks could resume and others pushing for a new vote.
The chancellor is skeptical about ruling without a parliamentary majority, and Schulz's conciliatory comments - after eight hours of talks among SPD leaders that went into early Friday - signal that his party may be willing to compromise.
Schulz had repeatedly rejected governing in Merkel's shadow, but has now faced mounting pressure within his party ranks to rethink his stance, and help stop Germany from sinking into months of paralysis.
Schulz' leadership could potentially be called into question at the party's conference in December in an attempt to rebuild from its poor showing at the election, with unnamed SPD figures telling German outlet Süddeutsche Zeitung that he would unlikely be the party's candidate were another election called.
"It is not the SPD that is responsible for this situation", he said.
The SPD was in government with Mrs Merkel in 2013-2017 and said it would not renew the deal following the 24 September election, when the party had its worst election result since 1949.