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

Stephen Allen, USAID's Disaster Assistance Response Team leader for the agency’s earthquake response, said his top priority is getting two American urban search and rescue teams to the region.

"Every hour does count in the first few days,” he said.

The responders are en route to Turkey, where they are expected to land at Incirlik Air Base in Adana Wednesday morning local time, Allen said. They’ll immediately start the long journey to Adıyaman, a city in southeastern Turkey that’s been heavily impacted by the quake, but has not had access to many search and rescue teams, Allen said.

The Americans are bringing about 170,000 pounds of specialized tools and equipment, including hydraulic concrete breaking gear, saws, torches, drills and advanced medical supplies to treat and triage the wounded, he said. They will also have about a dozen dogs who Allen said will play a “very key” role in looking for survivors strapped in the rubble.

Sending search and rescue teams to a disaster site so far away is “not something that we would normally do, frankly,” he said, however Turkey officials asked for assistance because its own considerable national search and rescue capabilities are outmatched by the “size and scale” of the devastation.

“I do need to emphasize the level of devastation, the level of damage, and the expected result in loss of life is massive. It’s massive,” he said.

-ABC News’ Shannon Crawford