"People are still leaving Ras al-Ayn as we speak", he said.
"President Erdogan and his regime must face serious consequences for mercilessly attacking our Kurdish allies in northern Syria", Republican Representative Liz Cheney, chairwoman of the House Republican Conference, said in a statement.
Trump said in a White House statement Wednesday: "This morning, Turkey, a North Atlantic Treaty Organisation member, invaded Syria".
Separately, the ministry said 49 more "terrorists" were "neutralized" in the incursion, in reference to Syrian Kurdish fighters.
Those numbers could not be independently verified.
"Turkey wouldn't consciously do anything that would cause the release of ISIS (another name for the IS group) fighters", Eissenstat said.More news: Former Ukraine envoy scheduled to testify in Trump impeachment probe
The Kurdish militia has fired dozens of mortars into border towns inside Turkey in the past two days, according to officials on the Turkish side.
The SDF said Turkish air strikes and shelling had killed nine civilians.
Ankara has long opposed U.S. support for the YPG in the fight against the militant Islamic State (IS) group, arguing the militia is a "terrorist" offshoot of Kurdish insurgents inside Turkey. Penalties will also be debated next week at the European Union leaders' meeting, France's EU Affairs Minister Amelie de Montchalin said on Friday.
The latest attack hit the town of Suruc, and a child in the town of Ceylanpinar died of his wounds Thursday night, the Anadolu Agency reported.
The Kurdish YPG is the main fighting element of the SDF which have acted as the principal allies of the United States in a campaign that recaptured territory held by the Islamic State group.
Syrian Kurds have vented their anger at what they see as a betrayal by Washingon with protests outside the US-led coalition bases dotted around the Kurdish-controlled northeast. Cavusoglu said Ankara expected "strong solidarity" from the alliance.
European countries "need to co-operate with Turkey on key issues, such as managing refugees", said Ozgur Unluhisarcikli, director of the German Marshall Fund's Ankara bureau.More news: Angelina Jolie's son is a 'good man'
Turkish officials say the returns would be voluntary, insisting that the operation will provide the stability needed to create an environment for resettlement.
Turkish President Tayyip Erdogan's communications director said that U.S. President Donald Trump, in a Sunday phone call which appeared to pave the way for Turkey's offensive, agreed "to transfer the leadership of the counter-Islamic State campaign to Turkey".
European diplomats in Brussels have responded cautiously to the idea of sanctions on Ankara, though the invasion has met with unanimous criticism. Now the Turkish army is going in, the Kurds are abandoning these camps.
He also plans to use the strip, which he envisions will be about 30 kilometres deep and is mostly Arab, as an area in which to send back some of the 3.6 million Syrian refugees who live on Turkish soil. The UN refugee agency said tens of thousands were on the move, and aid agencies warned that almost a half-million people near the border were at risk - in scenes similar to those from a few years ago, when civilians fled ISIS militants.
On Friday, Turkish jets and artillery struck around Syria's Ras al Ain, one of two border towns that have been the focus of the offensive.
It was not immediately clear if there were any injuries in the camp for displaced residents, located 12 kilometers, or 7 miles, from the border.More news: Vasek Pospisil drops tough match against Russia’s Daniil Medvedev at Shanghai Masters