The Turkish Defense Ministry released a statement on Saturday saying that Ras al-Ayn "has been brought under control", while Turkish news channels broadcast images of the town wreathed with plumes of smoke from a barrage of artillery fire.
"There has also been more heavy shelling on and around Tel Abyad today", he added.
Members of the Kurdish-Canadian community say the Turkish assault could upend the stability of a fragile region and roll back progress against militants affiliated with the Islamic State group. Aid agencies have warned of a humanitarian crisis, with almost a half-million people at risk in north-eastern Syria.
Turkey's offensive began days after U.S. President Donald Trump spoke by phone on Sunday with Turkish President Tayyip Erdogan and ordered U.S. troops to be moved out of the way.
Trump's move drew worldwide criticism that he was abandoning the Kurds, U.S. allies who had fought in recent years with the Americans to defeat ISIL in northeastern Syria.
US military officials denied lawmakers' accusations that Washington abandoned USA allies.
The ministry affirmed that "Turkish border outposts south of Suruc came under Dochka and mortar fire from the hills located approximately 1,000 meters southwest of a US observation post". Several surrounding villages have also been overtaken, the officials said.
U.S. Defense Secretary Mark Esper said Friday that Turkey would risk "serious consequences" if it doesn't cease its attacks and - while announcing that Trump will sign an executive order giving his administration broad authority to hit the country with sanctions - U.S. Treasury Secretary Steven Mnuchin claimed that "we can shut down the Turkish economy if we need to".
Turkey and its allied fighters began the offensive on Wednesday to push back the Kurdish Peoples' Protection Units (YPG), the backbone of the SDF, from its border.
Turkey's defence ministry said it "neutralized" 415 Syrian Kurdish fighters.
Turkey says its aim is to defeat the Kurdish YPG militia, which it sees as an enemy for its links to insurgents in Turkey.
Aksoy said the Turkish operation would proceed "with determination" in fighting "terrorist organizations" that are a threat to Turkey's national security.
Qatar and Somalia expressed reservations upon the statement that described the Turkish offensive as a breach of the UNSC 2254 resolution, which was adopted in December 2015 and calls for a ceasefire and a political settlement in Syria.
"We are not going to remain powerless in the face of this situation, which is a shock both for civilians and for Kurdish forces".
"We don't. negotiate with terrorists. The only thing to be done is for these terrorists to lay down arms", Cavusoglu told German broadcaster Deutsche Welle.
"The U.S. demands that Turkey avoids actions that could result in immediate defensive action".
The SDF's Qamishlo said the attack was carried out by IS sleeper cells and another senior SDF official said the Turkish assault had given new life to the jihadist group.
The risk that thousands of the militants they still hold could break free on the back of the Turkish operation could yet spur the global community into action.