Turkey's state-run Anadolu news agency earlier reported that four rockets fired from Syria hit the border town of Kilis overnight, damaging houses.
The U.S., however, has been offering military support to the Kurdish militia and even suggested days ago the establishment of a border security force in northern Syria to be dominated by Kurdish fighters, infuriating Turkey and chilling bilateral ties further.
But the YPG has been the key ally of Turkey's fellow North Atlantic Treaty Organisation member the United States in the fight against IS jihadists, playing a key role in pushing the extremists out of their Syrian strongholds.
Turkish ground troops have crossed into northern Syria as part of Ankara's campaign to rid the border area of Kurdish fighters, Turkey's PM says. On land, the Turkey-backed Free Syrian Army rebels were also helping the operation in Afrin, a senior Turkish official said.
But the recent escalation coincides with U.S. announcements that it is creating a new 30,000-strong Kurdish-led border force to secure the frontiers of Kurdish-controlled areas, including with Turkey and Iraq, to prevent the resurgence of Daesh militants.
A small unit from a Turkish-backed rebel group was manning a monitoring point on a hilltop overlooking several Kurdish-controlled villages below.
The attack comes on the heels of a week of sharp threats by the Turkish government, promising to clear the Kurdish People's Protection Units, or YPG, from Afrin and its surrounding countryside, also called Afrin.
A Turkish Government source explained to this newspaper that " necessary measures have been taken to avoid civilian casualties" and that Red Crescent has established camps to welcome population fleeing Afrin in population of Azaz, located in Syrian territory.More news: Rockets End Warriors Road Winning Streak
The U.S. coalition in Syria said this week the BSF will be built up "over the next several years" and "be stationed along the borders ... to include portions of the Euphrates river valley and worldwide borders to the east and north". However, Birusk Hasakeh of the YPG told AFP on Saturday that at least seven civilians - including a child - had been killed in airstrikes, along with three fighters; two female and one male.
But a YPG spokesman claimed Turkish forces seeking to enter Afrin had been "blocked" and that it had hit two Turkish tanks. They said they refused the proposal. "There is no need to worry".
The attacks follow weeks of warnings against the YPG in Syria from President Recep Tayyip Erdogan and his ministers.
The daily said Ankara has informed Damascus of its military operation in Afrin and cited Erdogan's statements that the operation will include Manbij.
A Turkish dvance on Manbij would further strains relations with Washington, which has troops operating in the Manbij area.
But even more crucial is the attitude of Russian Federation, which has a military presence in the area and is also working with Turkey on a drive to end the civil war.
"We always support Turkey". Russia, which has troops in the area, has urged restraint - an MP in Moscow says it will be discussed at the UN.
Washington has been concerned about a Turkish military incursion and called on Ankara to refrain from launching one.