The reported strikes came on the second day of "Operation Olive Branch," as Turkish tanks and troops rolled into Syria in an offensive against the area held by the Kurdish People's Protection Units (YPG), which Ankara considers a terror group.
The Britain-based Syrian Observatory for Human Rights said the dead, who included five children, were killed in air strikes on the village of Jalbara. It earlier gave a death toll of eight.
Observatory head Rami Abdel Rahman told AFP that eight of those killed were members of one family who had fled fighting in the northwestern province of Idlib.
Earlier a spokesman for the Kurdish forces that control the Afrin area also reported the raids.
Turkish ground forces have crossed the Syrian border into the Kurdish-held enclave of Afrin. (AAP) Source: AAP
"Eight civilians were killed in missile strikes on a chicken farm where they were living," said Birusk Hasakeh, a spokesman for the YPG in Afrin, blaming Turkish warplanes.
In pictures sent by Hasakeh to AFP, Kurdish Red Crescent rescuers could be seen retrieving bloodied bodies from a collapsed concrete structure and laying them on orange stretchers.
On Saturday, Hasakeh told AFP that Turkish bombardment had killed 10 people, including seven civilians.
Turkish Foreign Minister Mevlut Cavusoglu said Sunday that claims of civilian casualties from the offensive were untrue.
"As always, the PYD/YPG terrorists continue to deceive the world with nonsense propaganda and baseless lies by showing neutralised terrorists as civilians," he wrote on Twitter.
He was referring to the Kurdish Democratic Union Party and its armed wing, the YPG, fighting in Syria.
"They use civilians as human shields. Our target is neither our Kurdish brothers nor Syrians. We are only after terrorists."
And the Turkish army says it is doing everything possible to prevent civilian casualties.
"In the planning and execution of the operation only terrorists and their shelters, positions and weapons are being targeted," the army has said.
Troops enter
Turkish troops on Sunday crossed over the Syrian border into the Afrin region on the second day of Ankara's operation against the Peoples' Protection Units (YPG) Kurdish militia, Prime Minister Binali Yildirim said.
Yildirim told Turkish reporters in a briefing in Istanbul that the troops crossed into the YPG-controlled region in Syria at 0805 GMT from the Turkish village of Gulbaba.
The state-run Anadolu news agency said that the Turkish army troops, whose number was not specified, were advancing alongside forces from the pro-Ankara rebel Free Syrian Army (FSA).
A rebel commander told media around 25,000 Free Syrian Army rebels joined the Turkish military operation in northern Syria with the goal of recapturing Arab towns and villages seized by the YPG Kurdish militia almost two years ago.
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.
"We have no interest in entering the city only the military targets inside the city and the villages around it. We aim to encircle the city and ensure the militias are evicted. We won't fight in the city as we have no problem with civilians," he said.
Turkish forces on Saturday began a major new operation aimed at ousting the YPG from Afrin, pounding dozens of targets from the sky in air raids and with artillery.
Turkish Prime Minister Binali Yildirim was quoted as saying that the Turkish forces aimed to create a security zone some 30 kilometres (18 miles) deep inside Syria.
Turkey accuses the YPG of being the Syrian offshoot of the Kurdistan Workers' Party (PKK) which has waged a rebellion in the Turkish southeast for more than three decades and is regarded as a terror group by Ankara and its Western allies.
But the YPG has been the key ally of Turkey's fellow NATO member the United States in the fight against IS jihadists, playing a key role in pushing the extremists out of their Syrian strongholds.
US calls for restraint
The United States has called for Turkey to "exercise restraint" and avoid civilian casualties in its cross-border operation targeting the Syrian Kurdish forces.
The call came a day after Turkey launched the "Operation Olive Branch" offensive.
"We urge Turkey to exercise restraint and ensure that its military operations remain limited in scope and duration and scrupulous to avoid civilian casualties," State Department spokeswoman Heather Nauert said in a statement.
"We call on all parties to remain focused on the central goal of defeating" the Islamic State jihadist group, Nauert said.
