Freezing temperatures deepened the misery on Thursday for survivors of a massive earthquake in Turkey and Syria that killed more than 16,000 people, as rescuers raced to save countless people still trapped under rubble.

The death toll from Monday's 7.8-magnitude quake is expected to rise sharply as rescue efforts pass the 72-hour mark that disaster experts consider the most likely period to save lives.

Turkish President Recep Tayyip Erdogan on Wednesday conceded "shortcomings" after criticism of his government's response to the earthquake, one of the deadliest this century.

Survivors have been left to scramble for food and shelter – and in some cases watch helplessly as their relatives called for rescue, and eventually went silent under the debris.

Still, rescuers kept pulling survivors from the debris as the death toll continued to rise.

As criticism mounted online, Erdogan visited one of the hardest-hit spots, the quake's epicentre Kahramanmaras, and acknowledged problems in the response.

"Of course, there are shortcomings. The conditions are clear to see. It's not possible to be ready for a disaster like this," he said.

Officials and medics said 12,873 people had died in Turkey and at least 3,162 in neighbouring Syria from Monday's quake, bringing the total to 16,035.

In Syria, survivors said they felt alone in responding to the disaster.

"Even the buildings that haven't collapsed were severely damaged. There are now more people under the rubble than those above it," Hassan, who did not provide his full name, said in his rebel-held Syrian town of Jindayris.

The White Helmets, leading efforts to rescue people buried under rubble in rebel-held areas of Syria, have appealed for international help in their "race against time".

They have been toiling since the quake to pull survivors out from under the debris of dozens of flattened buildings in northwestern areas of war-torn Syria that remain outside the government's control.

A leading UN official has also called for the facilitation of aid access to rebel-held areas in the northwest, warning that relief stocks will soon be depleted.

"Put politics aside and let us do our humanitarian work," the UN's resident Syria coordinator El-Mostafa Benlamlih said. (AFP)