The European Commission is reiterating its call for Turkey to open the border near the southern town of Kilis, where more than 35,000 Syrians are waiting.
Many of the people have fled an escalating government assault on Aleppo.
Rebel-held areas in and around the city are still home to 350,000 people and aid workers have said they could soon fall to the government.
The Syrian Observatory for Human Rights, which monitors the war, said air strikes, thought to be from Russian planes, hit villages north of Aleppo on Sunday.
“There is a moral, if not also legal duty, to protect those in need of protection and asylum seekers, that arises out of the Geneva Convention,” said Mina Andreeva, EU Commission spokesperson.
Turkey finds itself in a difficult position. The country is already sheltering more than two and a half million Syrian refugees – a number that could swell further with the new arrivals.
At the same time, Ankara is being called upon by the EU to limit the flow of people to Europe and to readmit those who have had their asylum applications rejected elsewhere.
The Oncupinar gate on the border has been largely shut for nearly a year. The newest arrivals have been shepherded into camps on the Syrian side, where Turkey says they are safe for now.
The local governor of Oncupinar said on Saturday that around 35-thousand had reached the border in the space of 48 hours.
“If needed, we will let those brothers in,” President Recep Tayyip Erdogan was quoted as saying.
Aid officials at Oncupinar said they were focusing for now on getting aid to the Syrian side of the border, where Turkish agencies have set up new shelters.