Turkey says it 'won't strike' US-reinforced Syrian city
Prime Minister Binali Yildirim appeared to back down from previous to strike Kurdish militias based in the city, which lies close to the Turkish border.
Ankara views the Kurdish component of the US-backed Syrian Democratic Forces which holds Manbij as being a "terrorist entity".
"It makes no sense to launch an operation in Manbij without the cooperation of Russia and the United States," Yildirim told Turkey's A Haber and ATV television channels.
The news comes as Washington announced it would send more troops to Manbij, in a bid to defuse tensions between Washington's allies.
Both the Syrian Democratic Forces and Syrian rebels are engaged in offensives against the Islamic State group, which the US is working to defeat.
The Pentagon did not say how many troops would be sent, but armoured vehicles with US flags were already spotted in the Kurdish-held city last week.
With fighting continuing on Monday, the move will likely send out a stronger message to the warring Ankara-backed Syrian rebels and Kurdish forces to cease fire.
"We have brought in some additional forces to be able to do this reassurance and deterrence mission," said Defense Department spokesman Navy Captain Jeff Davis.
Manbij was captured by Kurdish-led forces in 2016 after fierce battles with the Islamic State group who previously occupied the city.
Now with neighbouring al-Bab retaken by Syrian rebels - with Turkish support - it has put them on a collision course with the neighbouring Kurdish canton in Manbij.
Ankara has said it wants to clear the Syrian-Turkish border of "hostile" Kurdish militias and IS elements.
Meanwhile, Washington is working to have these two competing powers turn their guns on IS and launch an offensive on the jihadi group's stronghold in Raqqa.
Russian forces also entered Manbij on the weekend, while it was reported that the Kurdish-led force in Manbij had agreed to a Moscow-brokered truce to hand the city over to the Syrian regime.
This scenario would likely anger the rebels, and possibly the US who see the Kurdish and Syrian opposition forces as willing to put up a stronger fight against IS than Damascus.
"This is obviously a really complicated situation," Davis said.
"We have made visible actions in deploying US forces as part of the coalition in and around Manbij to reassure and deter - that's to deter parties from attacking any other parties other than [IS] itself."
There are around 500 mostly special forces in northern Syria on a train-and-advise mission for anti-IS forces, mostly from the Syrian Democractic Forces.