According to state-run news agency Anadolu, Erdogan and Merkel are committed to "giving fresh impetus to bilateral contacts at the highest level", once a German government has been formed.
The call came a day after a similar call between Erdogan and German President Frank-Walter Steinmeier, Anadolu said.
Ties between the two countries -- NATO allies with strong historic ties - have nosedived over Ankara's arrest of German citizens and Berlin's strong criticism of the Turkish crackdown following last year's failed coup, which has seen over 50,000 people arrested.
The Turkish government has however sent several reassuring signals in recent weeks, including the conditional release of two German nationals who had been detained in Turkey.
A week after the German citizens were set free, the countries' foreign ministers also met in the southern Turkish resort of Antalya for informal talks -- the first meeting since the bitter row intensified.
During the call Thursday, Merkel and Erdogan discussed the pact signed last year between Ankara and the European Union, which has reduced the number of migrant and refugee routes to Europe, according to Anadolu.
Ankara has accused the EU of not granting the financial assistance promised under this agreement quickly enough.
Erdogan also briefed the chancellor on a Turkey-Iran-Russia summit on Syria, held last week in the Russian resort of Sochi, according to Anadolu.