"We will determine a date for the two presidents to meet in May before the NATO summit as previously confirmed by the leaders," Foreign Minister Mevlut Cavusoglu told reporters in Ankara.
The NATO summit is scheduled to be held in late May in Brussels and Trump is due to attend. Cavusoglu did not specify if the meeting would take place on the sidelines of the summit or at another venue.
Cavusoglu said that during their call the two leaders had expressed a common desire to meet in Washington "to improve bilateral relations".
Turkey hopes ties with the Trump administration will improve after relations soured between the NATO allies during Barack Obama's term over Syria and Turkey's calls for US-based Muslim cleric Fethullah Gulen to be extradited.
Gulen is accused of ordering last July's failed coup and Ankara has repeatedly called for his extradition. The preacher vehemently denies Turkey's accusations.
Tillerson met Turkish leaders and discussed the six-year Syrian civil war and the fight against the Islamic State group (IS).
The US believes Kurdish militia are the most effective fighting force against IS in Syria but Ankara claims they are terrorists linked to outlawed Kurdish militants waging an insurgency inside Turkey.
These tensions have cast a shadow over the relationship and also raised questions over whether Turkey would take part in any US-led operation to oust IS jihadists from their de- facto capital of Raqa.
"The way president Trump is approaching these matters makes us happy," he said.
"We can resolve significant problems. We do not have any difficulties on that front," Erdogan added.
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