President Donald Trump and Turkey's Recep Tayyip Erdogan have agreed to cooperate in the fight against militants in Syria, in their first phone call since the new US leader took office, Ankara said Wednesday.

The leaders of the two NATO allies also agreed that the new CIA chief, Mike Pompeo, would visit Turkey this week, a Turkish presidential source said.

In their eagerly awaited phone call late Tuesday, the presidents discussed acting together in Turkey's battle to capture the Syrian town of Al-Bab from the militant Islamic State (IS) group and taking the main IS stronghold of Raqa.

“Both leaders agreed to act together in Al-Bab and Raqa” in Syria, the source said.

A member of the US-led coalition against IS, Turkey in August launched a unilateral incursion in Syria, backing Syrian rebels to clear its border from IS militants and also pushing back Syrian Kurdish militia.

However, the battle for Al-Bab has proved the toughest yet of the Turkish incursion, with the army suffering increasing casualties and Erdogan complaining Ankara has been left alone.

Meanwhile a joint US-Turkey operation to take Raqa was mooted before but never developed further. Erdogan has high hopes of Trump after expressing disappointment in the past with the former US administration of Barack Obama.

Turkey was particularly enraged by US support for Syrian Kurdish militia which Washington regards as the most effective group in the fight against IS.

Turkey sees the Kurdish Democratic Union Party (PYD) and its armed wing, the Kurdish Peoples' Protection Units (YPG), a terror groups and branches of the outlawed Kurdistan Workers' Party (PKK) which has waged a bloody insurgency against the Turkish state since 1984.

In their phone call, Erdogan stressed the importance of the fight against the PKK and said that Washington should not support the PYD and YPG, according to the Turkish presidential source.

Erdogan also said Turkey expected Washington to stand by Ankara in the fight against the US-based preacher Fethullah Gulen who it accuses of staging the failed July 15 coup against Erdogan. Ankara charges Gulen runs a group called Fethullah Terror Organisation (FETO), something he denies.

The source also said that Central Intelligence Agency director Pompeo will visit Turkey Thursday which will be his first trip overseas since being sworn in January.

“He will consult with Turkish authorities' agenda items particularly the PYD and FETO,” the source said.

The White House said in their phone call Trump spoke of the “their shared commitment to combating terrorism in all its forms”, saying Trump reiterated US support to Turkey as a “strategic partner and NATO ally. “