But Turkey, which has already sheltered about 2.5 million people, is drawing world attention to Russian airstrikes driving people from what was formerly Syria's most populous city.
It comes as world leaders prepare to hold talks in Munich to resurrect Syrian peace talks.
Sirens sound on the streets of Aleppo, in the aftermath of the lastest aerial attack - reportedly by Russian planes.
On the ground, those that are left have little time to help the injured and check for the dead before government troops attempt to push out any remaining rebels from the strategic city.
Many Syrians have ended up at the Turkish border running west and north of Aleppo.
People seeking emergency help are allowed across immediately, like six year-old Aya al-Sharqawi.
She fled the town of Tel Rifaat, just north of Aleppo, with her uncle.
"I went out to buy biscuits. I was on my way to the shop. When the plane came I started running. I was near the entrance of my sister's house when the plane came and dropped a bomb."
Tens of thousands of people have made it to the Turkey-Syria border this week, but no further.
Turkey's Foreign Minister, Mevlut Cavosoglu, has defended his country's current border control policy.
"We talked about the Russian airstrikes. Because of them, more than 50,000 people escaped to the Turkish border, we admitted 10,000 but for the others we will set up camps on the other side of the border. We can only let them through in a controlled fashion. If airstrikes continue, the refugee flood could reach 100,000 or even one million."
Mr Cavosoglu has been in Budapest visiting his Hungarian counterpart, Peter Szijjarto.
Mr Szijjarto says Europe must protect its borders, insisting it's a matter of security.
"The daily influx of migrants worsens the public safety and increases the terror risk. This happens when thousands flow uncontrolled into the territory of the European Union without any security screening. We agreed to highlight the importance of the fight against terror and Turkey is facing a big risk of terrorism."
Turkish officials are deflecting the pressure towards Russia.
Turkish Prime Minister, Ahmet Davutoglu, says Turkey has not shut its gates to refugees but wants the international community to do more to stop Russian airstrikes on Aleppo.
"90 per cent of 6,000 Russian sorties have targeted civilians. All the international community, United States, and United Nations, know this. It has to be stopped. We expected the conscience of humanity to act but it has not happened. The heart of the international community has stopped, frozen."
UNHCR spokesman William Spindler agrees more effort is needed, saying pledges made by European leaders to resettle Syrian refugees have not been met.
"If half of the decisions and resolutions that have been taken by the European Union last year had been implemented, the situation now would be much better. For instance, a number of decisions were taken to relocate within Europe 160,000 people. So far, only about 400 have been relocated. Many European countries are not living up to their commitments. They need to be doing more, they need to be doing what they agreed to do."
The battle for Aleppo has stalled peace talks on the Syrian crisis.
A meeting is set for this week in Munich to try and resurrect the talks.
US Secretary of State John Kerry says it's important leaders continue to try to solve the Syrian crisis through diplomacy.
"This meeting will tell a lot about the road ahead. We are not blind to what is happening, we are all very very aware of how critical this moment is and Russia needs to contribute in significant ways to sustaining the ability of the opposition and others to come to the table to create an atmosphere within which you can actually have a negotiation."
But in Aleppo, there's no let in the fighting.
Syrian government forces - backed by the Russian airstrikes - keep up their attacks, with a senior adviser to President Bashar al-Assad saying the Syrian army aims to retake the city.
Rebels continue to fight Syrian government troops.
And opposition negotiators won't attend peace talks without a halt to the bombings.
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