It's a dramatic turnaround from her position just 10 days ago, as she faces pressure from her own party over her refusal to tighten Germany's border controls.
Emerging from talks in Istanbul, the German and Turkish leaders said positive progress had been made.
Turkish Prime Minister Ahmet Davutoglu said the two countries have agreed to work closely to resolve the migration crisis.
"We are ready to fight against illegal migration, against human traffickers who exploit desperate people. Turkey is ready for all kinds of cooperation with this regard. Immigration is a case but this should be legal and coordinated. Turkey and Germany will work shoulder-to-shoulder for legal and coordinated migration."
German Chancellor Angela Merkel says Germany will help accelerate the path to visa-free travel to the EU for Turks and push forward Turkey's bid for EU membership.
"Turkey and European Union agree that a closer cooperation is needed to tackle these problems. There is an agreement on accelerating Turkey's membership talks as well as visa liberation and readmission agreements."
In return, she wants Turkey to agree to take back people whose bids for asylum have been rejected by the European Union.
Ms Merkel is facing growing pressure to tighten Germany's border controls and turn away asylum seekers arriving from Austria.
Germany expects between 800,000 and one million new arrivals this year.
The European Union last week flagged additional funding for Turkey to help build facilities for the Syrians it has taken in.
It also said it would fast-track talks over Turkey's EU membership bid, and work on easing visa access for Turkish citizens travelling to the EU.
Meanwhile, large numbers of migrants are gathering on the Serbia-Croatia border, after Slovenia said it would limit the number of migrants crossing its borders to 2,500 per day.
Slovenian Interior Minister Bostjan Sefic says his country can only take half the number requested by Croatia, because Austria is only allowing 1,500 people in each day.
"We cannot accept a number of migrants larger than the number of those who will continue their journey. In a very short time, in maybe ten days, we would have 35,000 migrants in Slovenia, which is unacceptable for us."
Hungary closed its border with Croatia over the weekend in a bid to block the flood of people, after already sealing its border with its non-EU neighbour, Serbia, a month ago.
Meanwhile, more than 80 bishops from the Church of England have signed a letter calling on the British government to accept an extra 30,000 refugees from Syria.
But Britain's Defence Secretary, Michael Fallon, says no one's doing more than Britain to help Syrians who've been displaced by the conflict in their country.
"We've announced that we'll take 20,000 - 5,000 a year for the rest of this parliament which is a number we think we can reasonably accommodate, make sure they feel welcome, that they're given housing and the chance of getting a job here but the real issue is out in Syria. It's getting other countries in Europe to contribute more to the feeding of refugees in the camps and making sure their conditions are alleviated."
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