The officials spoke on condition of anonymity because they were not authorised to speak to the media.
Nouri Mahmoudi, another YPG official, also said: "all the Turkish military's ground attacks against Afrin have been repelled so far and they have been forced to retreat".
However this was the first confirmation that Turkish ground troops were now involved in the operation inside Syria.
A spokesman for the Kurdish militia that controls the area said that ten people had been killed in the attack.
Turkey considers the YPG a terrorist organization and has been infuriated by US support for the fighters.
Earlier this month, the Asharq Al-Awsat newspaper reported that the USA is planning steps toward providing a Syrian Democratic Forces-controlled area in northern Syria's eastern Euphrates area three times the size of Lebanon with diplomatic recognition.
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"We call on all parties to remain focused on the central goal of defeating" IS, State Department spokeswoman Heather Nauert said in a statement.
Major Yasser Abdul Rahim, who is also the commander of Failaq al Sham, a main FSA rebel group in the operations room of the campaign, said the rebels did not seek to enter the mainly Kurdish city of Afrin but encircle it and expel the YPG. The operation would force out the Kurdish militia from all positions west of the Euphrates River.
Mr Tillerson was reported on Wednesday denying that a border security force will be established, saying the issue has been "misportrayed".
The Turkish military says its offensive, named operation Olive Branch, aims to rid the region of the Kurdish People's Protection Units, or YPG. Ocalan is imprisoned by Turkey for waging a separatist movement in the eastern part of the country.
France on Sunday requested an urgent meeting of the UN Security Council to discuss ongoing developments in the Syrian areas of Afrin, Idlib and Ghouta, the country's Foreign Minister Jean-Yves Le Drian said in a tweet on Sunday. The military operation has already been condemned by Damascus with the Syrian Foreign Ministry calling the act a violation of Syrian sovereignty.
He said Turkey will turn over the region to "its real owners" once the intervention is completed and that there is no possibility of a clash with the U.S.in the field. No further details about the 30km security zone were given. Russian Federation was keeping military observers in Afrin and lately firmed up its ties with the YPG, while Syria's government in Damascus said it would shoot down any Turkish jets on raids in the country.
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"There are around 8,000 to 10,000 terrorists in Afrin", Yıldırım said.
The Air Forces also hit the Menagh Military Airbase in northwestern Syria, which the US used for supplying weapons to the YPG.
Also on Saturday, Syrian government forces and supporting militias retook a key air base in northwest Syria lost to rebels in 2015.
The Syrian Kurds wants to unite the two areas and create an autonomous state, similar to Iraqi Kurdistan in Iraq, where an independence referendum took place a year ago, which resulted in worsening tensions between Baghdad and the Kurdistan government.
But the advance, which began in earnest in late December, has displaced more than 200,000 civilians, according to the United Nations, exacerbating an already dire humanitarian situation in the north of the country.
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It turns out it's hard to run an offense with a bunch of players who've never played together before and mostly never will again. The game was played in front of a crowd of 21,700 inside Tropicana Field and was broadcast nationally on NFL Network.