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

The United States is “ramping up” assistance to Turkey and Syria, White House spokesperson John Kirby said Friday.

“In Turkey, a USAID Disaster Assistance and Response Team is already on the ground. And two of our most highly trained urban search and rescue teams are conducting operations in support of Turkish rescue efforts in Adana -- one of the hardest-hit areas inside the country,” Kirby said. “These teams have nearly 200 personnel combined between them, specialized equipment and canine support dogs, as well.”

Kirby said they’ve been able to “expand their operational reach with the support of U.S. military Blackhawk helicopters” to try and get around the extensive damage to roads and bridges.

“To date, they have been able to cover more than 630 sites across Adana [in Turkey],” Kirby said. “In Syria, our humanitarian partners continue to urgently scale up response efforts to reach people in need. That work will include, or has included, chartered flights that are transporting essential medical supplies and teams distributing hot meals and other food.”

The United Nations and its partners have successfully completed two humanitarian convoys into northwest Syria, Kirby said. One partner delivered 14 additional truckloads of supplies through the Bab-al-Hawa Crossing on the Turkey-Syria border, “totaling now 20 trucks of critical medicines, food and water to people in need over the last two days,” he said.

Kirby said U.S. sanctions imposed on Syria “will not prevent or inhibit prohibiting humanitarian assistance.”

-ABC News’ Justin Gomez