During the telephone call, the two leaders also vowed to improve bilateral relations, noting that Turkey and the US are two friendly and allied nations always connected to each other with links of alliance.
"The al-Bab operation must be completed immediately in the period ahead".
The two leaders discussed issues including a safe zone in Syria, the refugee crisis and the fight against terror, the sources said.
The operations to liberate the Syrian town of al-Bab had made important progress and the next target would be Raqqa, the de facto capital of ISIS, the Turkish Foreign Minister Mevlut Cavusoglu told a news conference in the capital Ankara.
"Ankara, just as us, speaks in favor of preserving the territorial integrity of the country and inadmissibility of its partition", he said.
Although Turkish troops have succeeded in clearing Turkey's borders of IS, the battle for al-Bab has proved a lot tougher both militarily and diplomatically, with Turkey and the United States at odds over the mission and its conduct.
Moreover, numerous new successful joint ventures between USA and Turkish firms aim to manufacture innovative products in Turkey for both domestic use and export to third country markets.
Ties between Turkey and the United States were troubled under the Obama administration.
Turkey sees the PYD and its armed wing, the YPG, as terrorist groups and branches of the PKK, outlawed in Turkey and blamed foran insurgency dating back to 1984.
During the US presidential campaign, Trump referred in glowing terms to Erdogan's handling of a failed coup attempt that shook Turkey last summer.
Ankara has been frustrated by Washington's reluctance to hand over the US -based Islamic preacher Fethullah Gülen, who is accused of masterminding the July 2016 coup attempt.
The Erdogan-Trump call came on the eve of a visit by CIA Director Mike Pompeo on Thursday, expected to also discuss the PYD/YPG and FETO. It will be his first trip overseas since being sworn in January.
While Turkey considers the PYD a terrorist group, the Obama administration described the PYD as a "reliable partner" in the fight against Daesh in Syria. The US president said during the conversation that he sees Turkey as a North Atlantic Treaty Organisation ally and a partner in the global war against ISIS terror.