Thousands of Syrians have travelled in freezing temperatures to Turkey's border after fleeing a government assault that threatens a new humanitarian disaster, with tens of thousands still trapped near the border on Monday.

Turkey sent in aid for the thousands of people stranded on the Syrian side of the closed border on Monday, saying it could not take in any more refugees.

"Turkey has reached the limit of its capacity to absorb the refugees," Deputy Prime Minister Numan Kurtulmus told CNN Turk television.

"But in the end, these people have nowhere else to go. Either they will die beneath the bombings... or we will open our borders."

Amid the massive displacement, huge numbers of people have been left to sleep outdoors in the cold winter weather.

"Thousands have been sleeping in the open, in fields and on roads," on the border and in the nearby Syrian city of Azaz, said Mamun al-Khatib, director of the Aleppo-based pro-rebel Shahba Press news agency.

"And because the main rebel supply route between Aleppo and Turkey has been cut, the price of oil, foodstuffs and baby milk has shot up in the north of Aleppo province," he added.

Activist Fadi Hajjar told Al Jazeera on Sunday that locals were preparing for Aleppo, which has been under partial rebel control since 2012, to be captured by the Syrian government and besieged.

Turkey's Oncupinar border crossing, which faces Bab al-Salama inside Syria, has remained closed over the weekend and on Monday, according to an Al Jazeera reporter at the border and AFP.

The UN said some 20,000 people had gathered at Bab al-Salama, but the governor of Turkey's Kilis border province, Suleyman Tapsiz, said at least 70,000 may head for the frontier.

According to the Britain-based Syrian Observatory for Human Rights, around 40,000 Syrian civilians have fled the government offensive in Aleppo, a figure that could not be independently verified by Middle East Eye.

On Sunday, Turkey said it was ready "if necessary" to let in tens of thousands of Syrians fleeing a major Russian-backed government offensive as aid agencies warned Sunday of a "desperate" situation.

"If they reached our door and have no other choice, if necessary, we have to and will let our brothers in," Turkish President Recep Tayyip Erdogan told reporters.

Turkish Foreign Minister Mevlut Cavusoglu has likewise said his country would keep its "open border policy" for Syrian refugees.

"We still keep this open border policy for these people fleeing from the aggression, from the regime as well as air strikes of Russia," he said.

"We have received already 5,000 of them; another 50,000 to 55,000 are on their way and we cannot leave them there."

Turkish Deputy Prime Minister Numan Kurtulmus also told CNN Turk on Sunday that Turkey would need to act.

"Turkey has reached the limit of its capacity to absorb the refugees," he said. "But in the end, these people have nowhere else to go. Either they will die beneath the bombings... or we will open our borders. We are not in a position to tell them not to come. If we do, we would be abandoning them to their deaths."

However, internal tensions in Turkey, which has long had one of the most open approaches to refugees, appear to be growing.

Residents in the southeast town of Kilis, which has become the only Syrian-majority town in Turkey, are warning that they can take in no fresh arrivals.

"I already feel I am not inTurkey," says Tugba Kaya, a Turkish nurse living in Kilia.

"It's like Syria here. Every step you take in Kilis you come across a Syrian. Life here would be paralysed in the face of a mass exodus," Kaya added.

Turkey's Oncupinar crossing into Syria much busier today - plenty of trucks entering, but no refugees allowed thru. pic.twitter.com/28WGrabE1P — Louisa Loveluck (@leloveluck) February 7, 2016

Turkish aid trucks and ambulances have also crossed into Syria to deliver food and supplies to people fleeing the joint government-Russian assault.

“We’re extending our efforts inside Syria to supply shelter, food and medical assistance to people. We are already setting up another camp,” an official from the Turkish Humanitarian Relief Foundation (IHH) told Reuters.

The EU has pledged more than $3bn in aid for Turkey, aimed at improving conditions for Syrians living in the country. A large aid conference in London last week also managed to secure several more billion in pledges, although donors have come under fire from some aid groups for pouring money in, in order to stop Syrians trying to reach Europe.

German Chancellor Angela Merkel is due in Ankara for talks over the issue on Monday.

435 killed as UAE mulls ground troops

According to the UK-based monitoring group, 124 government forces, 90 militants from al-Qaeda's Syria affiliate al-Nusra Front and 150 other rebels were also killed.

With the latest escalation on the ground, and peace talks suspended until later this month, pressure in the Gulf appears to be growing for a ground operation against IS.

The UAE on Sunday said it was mulling whether or not to send in troops and urged the US to lead an international ground coalition, something the US has been reluctant to do.

Syrian opposition sources revealed to Middle East Eye over the weekend that US Secretary of State John Kerry had all but abandoned the rebels and told them to brace for months more of heavy Russian bombing.

"Our position throughout is that a real campaign against Daesh [an alternative term for the Islamic State group] has to include ground elements," Minister of State for Foreign Affairs Anwar Gargash told reporters in Abu Dhabi.

"We are not talking about thousands of troops, but we are talking about troops on the ground that will lead the way," he said. "And of course, an American leadership in this effort is a prerequisite."

Riyadh on Thursday also said it would "contribute positively" if the US-led coalition against the Islamic State (IS) militant group in Syria decides on ground action.

Russia, a key ally of the Damascus government, has also accused Turkey of "preparations for an armed invasion" of Syria, a claim that Ankara dismissed.

Syria's Foreign Minister Walid Muallem issued a stiff warning against any such move on Saturday.

"Any ground intervention on Syrian territory without government authorisation would amount to an aggression that must be resisted," he said.

"Let no one think they can attack Syria or violate its sovereignty because I assure you any aggressor will return to their country in a wooden coffin, whether they be Saudis or Turks."

More than 260,000 people have been killed in Syria's conflict and more than half the population has been displaced.