Biden's National Security Adviser Jake Sullivan opened Tuesday's press briefing from the White House with an update on the president's response to the ongoing evacuations in Kabul, saying Biden has been in talks with top military commanders and his national security team from Camp David.

"They discussed the status of ongoing evacuations of U.S. citizens, SIV applicants and other vulnerable Afghans at risk, and how we would do this safely and efficiently," he said, adding Vice President Kamala Harris joined for some of those talks.

Reiterating points made in Biden's address to the nation Monday, Sullivan dug into the White House defense for withdrawing troops from America's longest war.

"The images from the past couple of days at the airport have been heartbreaking, but President Biden had to think about the human costs of the alternative path as well, which was to stay in the middle of the civil conflict in Afghanistan," he said.

Sullivan went on to argue that "what has unfolded over the past month has proven decisively that it would have taken a significant American troop presence multiple times greater than what President Biden was handed" to stop the Taliban, he said. "And we would have taken casualties."

The Taliban held its first-ever press conference from Kabul on Tuesday after claiming the formation of a new "Islamic Emirate" in Afghanistan.

ABC News Senior Foreign Correspondent Ian Pannell asked a Taliban spokesperson what guarantees it can give to the Afghans who worked with Americans and want to leave the country as the U.S. scrambles to evacuate thousands of allies who aided in the 20-year mission there.

"We are assuring the safety of all those who have worked with the United States and allied forces whether as interpreters or any other field that they have worked with them," said Taliban spokesperson Zabihullah Mujahid, translated from Arabic. "As for their talents and their skills, we do not want them to leave the country. We want them to serve our homeland."

He also acknowledged the case of American civil engineer Mark Frerichs, who is a hostage of the Taliban, though he didn't refer to Frerichs by name or offer any information on his whereabouts. It comes as Frerichs' family in the U.S. pleads with the Biden administration not to leave him behind.

"As for the contractor that was...perhaps has gone missing as reported by the media we do not have any information about him at the moment," Mujahid said.

The event was held at a media center in Kabul that was previously held by the Afghan government.

U.S. military commanders at Hamid Karzai International Airport have been in touch with Taliban leaders in Kabul multiple times a day, Pentagon press secretary John Kirby said in a briefing Tuesday morning.

"I would just let the results speak for themselves. I'm not going to get into the details of how those discussions are progressing because there are interactions multiple times a day," Kirby said of the talks. "There's been no hostile interactions from the Taliban to our operations at the airport," he added.

As for talks with Afghan allies, Kirby said he was unaware of any Pentagon-level communications recently.

"I know of no high-level communications here from the Pentagon with Afghan counterparts over the last couple of days," he said.

But Maj. Gen. William "Hank" Taylor, who joined Kirby at the podium, said military commanders are talking to Afghan National Security Forces, 500-600 of whom are helping the U.S. with airport security, despite the Taliban having toppled the capital.

The Taliban held a press conference in Kabul Tuesday and answered questions on the new "Islamic Emirate" it has claimed in Afghanistan.

Asked what assurances the Taliban can give to women and girls that the rights they've exercised for the past 20 years will be protected, Taliban spokesman Zabihullah Mujahid said, as translated from Arabic, "Women will be afforded all their rights."

"Whether it is at work or other activities, because women are a key part of society, and we are guaranteeing all their rights -- within the limits of Islam," he said.

When the Taliban last ruled, it enforced a strict version of Shariah -- or Islamic law -- and barred women from working or studying. Rina Amiri, a senior fellow at New York University's Center for Global Affairs and fellow at the Center for International Cooperation Rena Amiri, told ABC News Live earlier Tuesday that women have no reason to believe that will change now that the Taliban has seized back control.

"They're hiding in their homes because the Taliban has been coming to their doors. I've received so many calls where they have been intimidating them and their families," she said of the women in Afghanistan, fearful of the Taliban. "They're creating a climate of incredible repression and threat."

"What we see in Afghanistan is not a new Taliban that's better for women. We see one that's more strategic more brutal and far more effective," she added.

Amiri stressed that women who've been activists or leaders in the community are in imminent danger.

"It's laudable that the administration wants to help those that work directly for the U.S., but these are the U.S.'s strongest allies and supporters -- the women and the human rights defenders in the country -- and they are being abandoned, to a terrible fate," she said.