U.S. President Donald Trump has been accused of abandoning a loyal ally in the fight against IS after ordering American troops to pull back from the border.
Save the Children's Syria response director Sonia Khush said: "Once again, we urgently call on foreign governments to repatriate their nationals while they can".
According to Turkish media, Ankara aims to take control of a territory 120 kilometres (75 miles) long and 30 kilometres into Syria, up to the towns of Tal Abyad and Ras al-Ain.
Erdoğan said the Turkish-led forces had also besieged the Syrian border town of Tel Abyad, adding that two Turkish soldiers and 16 SNA members had been killed in the operation.
Reports of civilian casualties also surfaced.
The Britain-based Syrian Observatory for Human Rights said Turkish warplanes struck villages near the camp on Sunday. The SDF said a "civilian convoy" had been targeted.
"If the United States leaves us alone, we might ally with Russian Federation or Syria to end this".
The Kurdish-led Syrian Democratic Forces were a key USA ally in the war against the Islamic State group and drove the extremists from most of the territory they once held in north-eastern Syria. All of this is playing out exactly as we predicted, and we again urge President Erdogan to stop and go back to the status quo.
Turkey now faces threats of possible sanctions from North Atlantic Treaty Organisation ally the United States unless it calls off the incursion.
France and Germany on Saturday suspended arms exports to Turkey. The Arab League has denounced the operation. Last week, the country launched its long-threatened incursion into the country after Trump ordered a small contingent of about 50 U.S. troops to be pulled back from the border area amid a belief that a Turkish incursion was imminent. If you really mean it, the British should stop selling Turkey weapons, because a year ago Theresa May gave them planes and now they are using them against us.
The videoed killing and others that may have occurred off camera nearly certainly constitute a war crime, according to global law, and may breach one of the conditions Trump set for allowing the Turkish offensive to go ahead unhindered by US troops in the area.
Turkish-backed Syrian opposition fighters on pick-up trucks drive through Tal Abyad, Syria.
The officials, speaking on condition of anonymity, said the troops had moved because of concerns they could be caught in the middle of the Turkish offensive.
Along the front lines of Turkey's assault, Turkish forces and Syrian rebels entered Suluk some 10 km (6 miles) from Turkey's border, the Syrian Observatory said on Sunday. Anadolu says one person was wounded in Suruc on Sunday. "They haven't helped us fight for our land", Mr Trump said.
NZZ am Sonntag says the whereabouts of Swiss Jihadists, some of whom are being held in northern Syria, is not clear. The force swept up thousands of Islamic State fighters and their family members in the campaign, and has warned it may not be able to maintain its various detention centres as it struggles to repel the Turkish advance.
Syrian Kurdish officials say Islamic-State supporters have escaped from a camp for displaced people in northeastern Syria after shells landed nearby. The M4 highway is also an important conduit for the limited amounts of aid reaching northeast Syria, and with a portion of the highway now under Turkish control, future aid supplies are at risk.
"Now the SDF's attack has started and there are very fierce clashes", he told Reuters.