The migrants’ boat capsized a short distance from the Greek island of Lesbos, with at least 23 people, including children, killed. Another 13 are missing, while four were rescued.
The Turkish news agency Dogan reported a separate incident in which it said 11 migrants were reported to have died when their boat sank.
In Ankara, Mrs Merkel said she was “shocked” and “appalled” by air strikes in the Syrian city of Aleppo, for which Russian forces, allied to the Assad regime, bore some responsibility.
She said the strikes were a breach of a UN Security Council from December, which calls on all sides in the Syrian civil war to avoid attacks on civilians.
The attacks in Aleppo have driven almost 30,000 Syrians to the Turkish border, where they are stranded. So far, the only people who have been allowed to cross are those have been injured. They have been receiving treatment in Kilis hospital.
Turkish aid agencies have been setting up temporary shelters and delivering food to Syrians waiting at the border.
At a news conference with Mrs Merkel, Turkish Prime Minister Ahmet Davutoglu said others would be allowed to cross “when necessary”.
Mrs Merkel said 3 billion euros was being made available to Turkey by the EU to improve refugees’ lives and they “have to see the benefits quickly”.
Mr Davutoglu said Turkey would inform Brussels next week how the money would be spent. The cash is designed to stem the record flow of migrants from Turkey to the EU.
On Sunday, France and Germany agreed an EU action plan that involves assistance to Greece to control its borders and combat people smuggling.