Turkey’s invasion of northern Syria created a humanitarian crisis that by Tuesday had displaced up to hundreds of thousands of civilians, according to Kurdish authorities and several humanitarian groups tracking the conflict.

The United Nations, meanwhile, was investigating whether Turkish troops and their Syrian allies committed war crimes by executing captured Kurdish fighters and civilians.

The UN Office for the Coordination of Humanitarian Affairs said at least 160,000 people had been forced out of their homes since Turkish President Recep Tayyip Erdogan launched the military offensive last Wednesday, days after President Trump ordered US troops to retreat from the area.

Other humanitarian groups put the number far higher.

The London-based Syrian Observatory for Human Rights said roughly 250,000 people have fled and 71 civilians, including 21 children, have been killed.

The Kurdish-led administration that controls that swath of territory in Syria said the fighting has displaced more than 275,000 people, including 70,000 children.

The UN High Commission on Human Rights said Turkey could be responsible for its troops or allies executing captured Kurdish fighters and a politician.

UN human rights spokesman Rupert Colville said video footage appears to show the execution of three Kurdish fighters by Turkish-affiliated forces on Saturday. And the UN is investigating whether Hevrin Khalaf, a female Kurdish politician, was executed the same day.

“Turkey could be deemed responsible as a state for violations by their affiliated groups as long as Turkey exercises effective control of these groups or the operations in the course of which those violations occurred,” Colville said Tuesday, adding that Turkish officials need to begin an “impartial, transparent and independent ­investigation.”

Meanwhile, Turkey shrugged off US sanctions and pressed on with its offensive while the Russian-backed Syrian army roared into one of the most hotly contested cities abandoned by US forces.

Russian and Syrian flags flew from a building on the outskirts of Manbij, and from a convoy of military vehicles.

Russia’s Interfax news agency, citing Moscow’s Defense Ministry, said later that Syrian forces had taken control of an area of more than 385 square miles around Manbij.

A week after reversing US policy and moving troops out of the way to allow Turkey to attack Washington’s Syrian allies, Team Trump on Monday announced a package of sanctions to punish Ankara.

But the measures mainly included a hike in steel tariffs and a pause in trade talks.

With Post wires