Rescuers pulled children from the rubble of the Turkey-Syria earthquake on Saturday as the death toll approached 24,000 and a winter freeze compounded the suffering of millions of people, many in desperate need of aid.

At least 870,000 people urgently needed food in the two countries after the quake, which has made up to 5.3 million people homeless in Syria alone, the UN warned.

Aftershocks following Monday's 7.8-magnitude tremor have added to the death toll and further upended the lives of survivors.

"When I see the destroyed buildings, the bodies, it's not that I can't see where I will be in two or three years -- I can't imagine where I'll be tomorrow," said Fidan Turan, a pensioner in Turkey's southern city of Antakya, her eyes filling with tears.

"We've lost 60 of our extended family members," she said. "Sixty! What can I say? It's God's will."

The United Nations World Food Programme appealed for $77 million to provide food rations to at least 590,000 newly displaced people in Turkey and 284,000 in Syria.

Of those, 545,000 were internally displaced people and 45,000 were refugees, it said.

• Humanitarian access -

The UN rights office on Friday urged all actors in the affected area -- where Kurdish militants and Syrian rebels operate -- to allow humanitarian access.

The outlawed Kurdistan Workers' Party, which is considered a terrorist group by Ankara and its Western allies, announced a temporary halt in fighting to ease recovery work.

In rebel-held northwestern Syria, about four million people rely on humanitarian aid but there have been no aid deliveries from government-controlled areas in three weeks.

The Syrian government said it had approved the delivery of humanitarian aid to quake-hit areas outside its control.

Only two aid convoys have crossed the border this week from Turkey, where authorities are engaged in an even bigger quake relief operation of their own.

A decade of civil war and Syrian-Russian aerial bombardment had already destroyed hospitals and created shortages of electricity and water.

UN Secretary-General Antonio Guterres urged the Security Council to authorise the opening of new cross-border humanitarian aid points between Turkey and Syria. The council will meet to discuss Syria, possibly early next week.

Turkey said it was working on opening two new routes into rebel-held parts of Syria.

The winter freeze has left thousands of people either spending nights in their cars or huddling around makeshift fires that have become ubiquitous across the quake-hit region.

• Anger builds -

Five days of grief and anguish have been slowly building into rage at the poor quality of buildings as well as the Turkish government's response to the country's most dire disaster in nearly a century.

Officials in the country say 12,141 buildings were either destroyed or seriously damaged in the earthquake.

"The floors are piling on top of each other," said Mustafa Erdik, a professor at Istanbul-based Bogazici University, which means the chances of being found alive are slim.

Police on Friday detained a contractor trying to flee the country after his building collapsed in the catastrophic quake.

The tremor was the most powerful and deadliest since 33,000 people died in a 7.8-magnitude tremor in 1939.

Officials and medics said 20,318 people had died in Turkey and 3,553 in Syria. The confirmed total now stands at 23,871.

Anger has mounted over the Turkish government's handling of the disaster, changing the tenor of the country's presidential election campaign ahead of polls due in June.

"People who didn't die from the earthquake were left to die in the cold," Hakan Tanriverdi told AFP in Adiyaman province.

Turkish President Recep Tayyip Erdogan conceded for the first time on Friday that his government was not able to reach and help the victims "as quickly as we had desired".

• Cypriot children -

One of the single biggest tragedies involved 24 Cypriot children between the ages of 11 and 14 who were in Turkey for a volleyball tournament when the quake swallowed their hotel.

Ten of their bodies were repatriated to their homeland in northern Cyprus.

Turkish media reported that at least 19 people in the group -- which included 15 accompanying adults -- have now been confirmed dead.