The US president telephones his Turkish counterpart to express congratulations.
The call came a day after more than 51 percent of Turks voted in favor of 18 constitutional amendments that will, among other things, see Turkey switch from a parliamentary to a presidential system of governance.
The two leaders also discussed a Syrian regime's chemical attack April 4 that killed approximately 100 civilians and injured 500 others in the opposition-held town of Khan Sheikhun in Idlib province.
Investigators in Turkey and elsewhere believe sarin gas was used in the attack.
Trump and Erdogan agreed Syrian President Bashar al-Assad is responsible for the attack.
The American president also thanked Turkey for its support for U.S. missile strikes on an Assad regime air base in retaliation for the chemical attack as both men stressed the need for cooperation on the fight against terror groups, including Daesh.