ISTANBUL (Reuters) - An agreement with the United States for the removal of a Kurdish militia from the northern Syrian town of Manbij needs to completed by the end of the year, Turkey said on Friday, voicing frustration with what it says is a deal beset by delays.

Turkey's Foreign Minister Mevlut Cavusoglu attends a news conference in Ankara, Turkey November 22, 2018. Cem Ozdel/Turkish Foreign Ministry/Handout via REUTERS

Turkey and the United States, both NATO allies, have seen their relationship strained by differences over Syria policy. Washington has backed the YPG Kurdish militia in the fight against Islamic State. Turkey says the YPG is a terrorist group and an extension of the outlawed Kurdistan Workers Party (PKK).

In May they reached a deal over Manbij, after months of disagreement, under which Kurdish fighters are to completely withdraw from the town - something Turkey says has yet to happen.

This month, Turkish and U.S. troops began joint patrols in the region. That cooperation has been complicated as Turkey has shelled Kurdish fighters to the east of the Euphrates, across the river from Manbij, and threatened an offensive there.

“This delay should not exist anymore. This issue needs to be completed by the end of the year,” Foreign Minister Mevlut Cavusoglu told broadcaster CNN Turk, referring to the withdrawal of the YPG from Manbij.

“Joint patrols have begun in Manbij and YPG needs to withdraw immediately from here. When we start implementing the same roadmap on the east of the Euphrates as well, YPG/PKK will be thrown out of all the cities,” he said.

The YPG are the core of a force that has fought against Islamic State with the support of U.S. air power, arms, funds, training and an estimated 2,000 American special forces troops on the ground.

Turkey has already intervened to sweep YPG fighters from territory west of the Euphrates in military campaigns over the past two years, but has not gone east of the river, in part to avoid direct confrontation with Washington.

However, Turkish President Tayyip Erdogan has more recently signalled that Turkey was ready to expand operations.

The YPG still controls are large swathe of northeast Syria, on Turkey’s southern border. Turkey fears the YPG’s presence across its border could fuel a Kurdish insurgency at home.

More than 40,000 people, most of them Kurds, have died since the autonomy-seeking PKK first took up arms against the Turkish state in 1984.