He said a convoy of 20 armoured vehicles carrying Syrian rebels entered Syria from Ceylanpinar on Friday.
Some 120 kilometres west, Turkish howitzers resumed shelling near the Syrian town of Tel Abyad, a witness said.
Turkish cross-border artillery fire hit a northern Syria town where a U.S. Special Forces unit was operating as fighting escalated between the invading Turkish military and the U.S. -backed Syrian Democratic Forces, according to a Newsweek report Friday.
In a later report they said that seven members of the pro-Turkish forces had been killed as the SDF retook a village in Tal Abyad region, one of them a Turkish soldier. It says it has killed 277 militants in total.
Ankara says the objective of its assault it to defeat the Kurdish YPG militia - the main component of the Syrian Democratic Forces (SDF) - which it designates as a terrorist group over its links to insurgents in Turkey.
"There is heavy fighting between the SDF and the Turks on different fronts, mostly from Tal Abyad to Ras al-Ain", the Syria Observatory for Human Rights said.
North Atlantic Treaty Organisation member Turkey considers the Syrian Kurdish fighters to be terrorists linked to a Kurdish insurgency inside Turkey and says the offensive is a counterterrorism operation necessary for its own national security.
Turkey wants to create a "safe zone" running for 480 km along the Syrian side of the border but says it will not be better than planned 32 km (20 - mile) limit.
He stressed that United States troops continue to work with SDF forces in areas away from the border region.
The Turkish invasion also has raised the prospect of losing control of thousands of captured Islamic State fighters.
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The Britain-based Syrian Observatory for Human rights reported that people had begun fleeing the border town of Tal Abyad. Turkey has said it intends to create a " safe zone " in order to return millions of refugees to Syrian soil.
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The letter comes the same day that Trump intensified his fight with Congress by blocking Gordon Sondland , the U.S. European Union ambassador, from testifying behind closed doors about the president's dealings with Ukraine.
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She says the evidence right now points to people getting sick from smoking products they bought from unauthorized retailers. Under FDA rules, only products that represent a net benefit to public health will be allowed to remain on the market.
A USA official, speaking on condition of anonymity to brief reporters, said the patrol was not in support of operations against the Turkish offensive.
At the White House on Friday, Treasury Secretary Steven Mnuchin put Turkey on notice that it could face "powerful sanctions" for its military offensive, saying that the USA will "shut down the Turkish economy" if Ankara goes too far.
The Pentagon on Friday urged Turkey to halt its military incursion into Syria, saying it threatens progress in combating the ISIS terror group and could put US troops in harm's way.
Trump said he did not think Americans wanted to see the USA military sent back into the region.
At least five people, including a Syrian baby, were reportedly killed in Kurdish shelling of Turkish border towns.
Humanitarian relief agencies have been providing food, water, medicine and other lifesaving aid to more than 90,000 internally displaced people there as well as more than one million other residents who had lost access to social services because of the conflict.
Darbasiya, some 60km to the east, was also reported to be largely deserted following the exodus.
"We are not abandoning our Kurdish partner forces", he said. It's unclear how far the Turks will take their offensive, how badly the Kurds will be hit and whether US forces will be compelled to withdraw entirely in coming days.
In a strong statement of support for the Kurds, Mr Esper insisted that "we are not abandoning our Kurdish partner forces, and U.S. troops remain with them in other parts of Syria".
Meanwhile, around 30 US House Republicans are expected to introduce a bill to push for sanctions against Turkey.
So the Europeans issued their own statement after the meeting, urging Turkey "to cease the unilateral military action".