Europe's economic powerhouse has been mired in uncertainty since Merkel's conservative bloc won a September 24th vote but without a clear majority.
"Europe needs a strong Germany... that's why it is important to form a government very soon," Merkel said in a speech to regional representatives of her CDU party in Kuehlungsborn, northeast Germany.
The speech came a day after the SPD said they were ready for talks with Merkel's bloc.
The European Union has been worried by the German crisis, as Berlin plays a lead role in all matters including the Brexit negotiations.
The setbacks Merkel's bloc suffered in the September election were in part due to the rise of the far-right, anti-immigration AfD which took millions of votes from mainstream parties.
Since the vote, Merkel has failed to find coalition partners to govern the EU's largest economy for her fourth term.
The centre-left SPD -- Merkel's former junior coalition allies -- vowed to go into opposition immediately after the election in which they scored a dismal result.
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.
Few good options
Merkel now faces few good options short of new elections: asking the SPD to enter a new "grand coalition", or running a minority government, possibly with the Greens, and asking the SPD to cooperate on an issue-by-issue basis.
For now, Merkel's caretaker government has continued to run the country's daily business.
President Frank-Walter Steinmeier, himself an SPD member, meanwhile has been working to ensure a compromise is reached, to avoid a repeat vote.
Talks with the SPD should be based "on mutual respect" and "compromise", Merkel said.
Chancellor of Germany since 2005, Merkel's party ruled alongside the SPD up to 2009 and then again from 2013 to 2017.
Steinmeier will on Thursday meet Merkel and the leader of the CSU -- the CDU's wing in Bavaria -- Horst Seehofer, as well as SPD leader Martin Schulz, the European Parliament's ex-president.
Merkel reiterated her opposition to a return to the polls.
"We have received a mandate" from voters, she said.
Polls show that, were Germany to stage an election re-run, results would be little different from September.
If anything, it could see the AfD score an even more impressive result than it did the first time round.