Turkish Prime Minister Binali Yildirim said last Sunday that the military operation aimed to establish a 30-km-deep security zone in Syria's Afrin.
Trump said in response to Erdogan's call on the United States to end the delivery of weapons to the YPG that the United States no longer supplied the group with weapons and pledged not to resume the weapons delivery in the future, the source said.
NATO Secretary-General Jens Stoltenberg defended Turkey's military action but urged caution.
He is urging Turkey to limit military activity in the region.
Operation "Olive Branch" in Afrin, a Kurdish-held area close to the Turkish border, was launched on Saturday.
"Azerbaijan as a country that has suffered from terrorism, resolutely denounces terrorism in all its forms and manifestations, and it defends efforts by the global community in this fight", Haciyev said, according to Azerbaijan Press Agency.
A push towards Manbij, in a separate Kurdish-held enclave some 100 km (60 miles) east of Afrin, could threaten U.S. plans to stabilise a swath of northeast Syria.
Any move toward Manbij would take North Atlantic Treaty Organisation member Turkey and its Syrian allies closer to US forces, threatening friction.
USA support for the YPG has infuriated Washington's North Atlantic Treaty Organisation ally Turkey, which sees the YPG as a terrorist group and has vowed to crush it.
Erdogan said the Turkish Army and allied Syrian rebels had lost seven or eight fighters in the ongoing offensive.
"If the United States doesn't stop this, we will stop it", Turkish Foreign Minister Mevlut Cavusoglu was quoted as saying on Tuesday.
Shervan Derwish, a spokesman for the Manbij Military Council, said his forces are on "full alert" in case Turkey moves on the city, where US-led coalition forces are still present. "Early on, Trump needs to do what Obama didn't do, which is to standup in Syria and say, 'No, this is where the US put its foot down'".
"Russian representatives are staying in contact with both the Syrian leadership and the Turkish leadership on this issue too", Peskov said. According to reports by Iran's Press TV, Baqeri said that Turkey must give assurances that it does not crave for any part of the Syrian soil.