"Turkish attacks in the north and IS attacks in the south against our troops had forced us to stop our current operation temporarily against ISIS in the last pocket of it", the SDF said in a statement.
The US and the Turks have been conducting independent patrols along the front line.
"We're fully supportive of the road map and the combined joint patrols, and I am confident they will be very effective", British Maj.
The YPG, the dominant group and leader of the US -allied Syrian Democratic Forces (SDF), controls almost all of the territory east of the Euphrates, including regions along Syria's border with Turkey.
USA relations with Turkey, one of its closest allies in the Middle East for decades, have been strained nearly to breaking point in recent months by differences over Syria, Iran and Ankara's planned purchase of Russian military equipment.
Earlier this year, the Turkish military conducted an offensive against the Kurdish militia in Syria's northern border region of Afrin.
Turkish and USA troops on Thursday began their first round of joint patrols in the northern Syrian city of Manbij, as part of a deal to rid the area of the YPG/PKK terrorist group, Turkey's national defense minister announced. Joint patrols are considered a way to tamp down potential violence between the various groups in the region.
"Unilateral military strikes into northwest Syria by any party, particularly as American personnel may be present or in the vicinity, are of great concern to us", State Department spokesman Robert Palladino told reporters on Wednesday.
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He can spend time with his family, then it's global break and then he will be back". Guardiola said at the final whistle: "He is being checked by the doctors.
FILE - In this April 4, 2018 file photo, a USA soldier sits in an armored vehicle on a road leading to the tense front line with Turkish-backed fighters, in Manbij, north Syria.
In an effort to alleviate the situation, the US agreed to jointly control Manbij with Turkish forces, and Kurdish forces agreed to withdraw.
"We will soon crush the terror organization in the east of the Euphrates with more comprehensive and effective operations".
On Sunday, the Turkish military fired artillery shells at US-backed Syrian Kurdish People's Protection Unit (YPG) positions in the east of the Euphrates.
"We have finished all our preparations [and] plans ... regarding the issue", Erdogan added.
"Ankara thinks that the terror groups on the eastern part of the Euphrates are undermining Syria's unitary structure and threatening Turkey's territorial integrity", he told Arab News.
Past offensives halted at the banks of the river, in part to avoid direct confrontation with the United States.