In a separate statement on Twitter,SDF spokesman Mustafa Bali said that Turkey's military hit a civilian convoy also near Tel Abyad,about 400 metres from the Turkish frontier,killing three.
Turkey views the Syrian Kurdish fighters as terrorists because of their links to Turkey's Kurdistan Workers'Party,or PKK,which has waged a decade-long battle in south-eastern Turkey for greater autonomy.
It launched its long-expected offensive targeting the SDF in north-eastern Syria Wednesday,with airstrikes and shelling targeting its outposts along the border.
Mortar fire from Syria landed in at least two Turkish towns,Turkish media reported.
The Turkish foray threatens to further fracture a war-shattered Syria,which has been devastated by a years-long conflict.
People wave Turkish flags in support of Turkish soldiers crossing the border into Syria.Credit:Getty Images
Turkish officials said the Kurdish militia has fired dozens of mortars into Turkish border towns the past two days,including Akcakale.
Turkish officials in two border provinces said mortar fire from Syria killed at least six civilians,including a 9-month-old boy and three girls under 15. On the Syrian side,seven civilians and eight Kurdish fighters have been killed since the operation began,according to activists in Syria.
Mikael Mohammad,a shop owner from Tel Abyad,fled the town with his family on Wednesday and slept in the open air in the countryside,he said.
"I had to leave with only the clothes I had on me,"he said in a telephone interview."I immediately got in the car,picked up my family and drove ... away from the border."
"Everything I rebuilt in the last few years,I may have just lost again,"Mohammad said.
"The shelling is barbaric and indiscriminate."
The Syrian Observatory for Human Rights said that 16 SDF fighters had been killed since the operation began on Wednesday,including in Ras al-Ayn,which is 120 kilometres east of Tel Abyad.
Nawras,a resident of Ras al-Ayn,described a night of intense shelling. Air strikes resumed in the morning,he said,prompting him and his family to flee.
"People are still leaving Ras al-Ayn as we speak,"said Nawras,an electrician."I'm being told that the city is still being targeted and that we should not consider going back for now."
Turkey's President Recep Tayyip Erdogan speaks to his ruling party officials in Ankara.Credit:AP
The past weeks have seen a buildup of Turkish forces on the border,belligerent speeches by Turkish officials and dire warnings from Turkey's NATO allies and others.
President Donald Trump called the Turkish offensive"a bad idea,"but also stood by his decision to pull back US forces to effectively clear the way for Turkey.
"Turkey has committed to protecting civilians,protecting religious minorities,including Christians,and ensuring no humanitarian crisis takes place,"he added."We will hold them to this commitment."
The offensive has presented the Trump administration with a dilemma as it has sought to balance Washington's partnership with Turkey and its links to the Syrian Kurdish forces that helped beat back the Islamic State.
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Erdogan's government has watched nervously for years as Syria's Kurds have built an autonomous enclave along Turkey's border. It railed against the United States for relying on the Kurds as a military partner and bristled as its enemies accumulated weapons and territory.
For years,the United States and Turkey have been engaged in negotiations aimed at soothing Ankara's security concerns.
There was also the risk that American troops still positioned in Syria could get caught in the crossfire.
A US official said the Trump administration had provided Turkey with a list of no-strike locations where US personnel were stationed.
The Washington Post with AP