The total number of deaths in Turkey and Syria rose to at least 41,219 on Tuesday.

There were 35,418 people killed in Turkey, according to President Recep Tayyip Erdogan. In Syria, the death toll currently stands at 5,801 in both government- and rebel-controlled areas of northwestern Syria, according to combined figures from the Syrian Ministry of Health and the Syrian civil defense and medical group that operates in opposition-held areas, known as the White Helmets.

The death toll in Turkey is now more than the 1939 Erzincan earthquake, the previous record for most deaths due to an earthquake in modern Turkish history.

One week after a devastating earthquake hit Turkey and Syria, millions of children remain in need of urgent humanitarian assistance, according to a report from UNICEF.

Roughly 4.6 million children are living in quake affected areas in Turkey and another 2.5 million children are living in the affected areas of Syria, the agency said.

UNICEF officials said the number of children killed and injured during the quakes hasn't been confirmed but is "likely to be in the many thousands."

The agency said there hundreds of thousands of families who lost their homes, and many are left in the cold with little infrastructure support.

"We must do everything in our power to ensure that everyone who survived this catastrophe receives life-saving support, including safe water, sanitation, critical nutrition and health supplies, and support for children's mental health. Not only now, but over the long term," UNICEF Executive Director Catherine Russell said in a statement.

-ABC News' William Gretsky

Syria has opened two more border crossings from Turkey for the next three months to help with the influx of humanitarian aid, according to the United Nations.

"Delivering food, health, nutrition, protection, shelter, winter supplies and other life-saving supplies to all the millions of people affected is of the utmost urgency," U.N. Secretary-General António Guterres said in a statement. "Opening these crossing points -- along with facilitating humanitarian access, accelerating visa approvals and easing travel between hubs -- will allow more aid to go in, faster."

Last week's massive earthquake and powerful aftershocks have killed at least 31,643 people in southeastern Turkey, according to the latest figures from the Turkish Disaster and Emergency Management Authority.

Meanwhile, at least 5,714 people were killed in both government- and rebel-controlled areas of northwestern Syria, according to combined figures from the Syrian Ministry of Health and the Syrian civil defense and medical group that operates in opposition-held areas, known as the White Helmets.

-ABC News' Will Gretsky and Joe Simonetti

More than 24 hours after devastating earthquakes, ABC News reporters on the ground are witnessing the fevered effort to rescue survivors at a collapsed apartment building in southeastern Turkish city of Diyarbakir.

ABC News learned that crews had recently rescued a woman from what used to be an eight-story apartment building, where the top half now rests on three flattened floors below. The front wall had fallen away, exposing what used to be homes with furniture, pillows and air conditioning units.

In and around the collapsed building, there was a flurry of activity -- but then a moment when it all came to a grinding halt. Generators were turned off, everyone stopped talking and the block went silent. Search and rescue teams thought they may have found another survivor. It was quiet for several minutes, but then the urgent effort returns.

Rescuers continued working in the cold, wet weather while also facing the threat of aftershocks. None of that has deterred them. They know this is a race against time.

-ABC News’ Engin Bas, Ibtissem Guenfoud and Marcus Moore