Former Army Ranger Jariko Denman, appearing on ABC's "This Week" Sunday, described his being in Kabul with other veterans to help evacuate Afghan allies and their families and his leaving just 30 minutes before the deadly attack at the Abbey Gate.

"You immediately went to Kabul to try to help with this network of veterans and others," "This Week" co-anchor Martha Raddatz said. "How does it even work?"

"When I flew in on the Ark Salus flight that I flew in on, I was surprised we got in because it was just -- no one had ever done it before. It was the first charter flight that we made and I didn't know if it would work," Denman said. "And then when it did, I didn't know if someone would be at the plane to tell me not to get off. I got off. I didn't know where I would stay and just started to figure it out. And that's what everyone back home was doing was figuring it out, figuring out how to communicate with each other, figuring out the most efficient ways of getting to these gates and -- and pulling our friends out."

"I know you worked with some of those Marines and Navy Corpsman we lost," Raddatz said. "This is a tough one for you. You've been in combat. You've lost a lot of friends. This is a tough one."

"Yes. Again, it was different going in with this lens. Those Marines and airmen and soldiers on that line and at those gates were just -- they were kids, and I was out there and tried to cheer them up," Denman said. "And, you know, they helped me so much getting -- getting my people that I was trying to pull out and getting the people that other people asked me to pull out. And, yes, no complaining. Just no, you know, 'screw these people.' None of that. It was all, 'we need to get as many out.' 'Just one more. Just one more.' And they're absolute heroes."

With their right hands placed over their hearts, the president and first lady Jill Biden attended a solemn ceremony at Dover Air Force Base as the remains of 13 service members killed in a suicide bomb attack at the gates of the Kabul airport were returned to the United States.

It was the first time as commander in chief that Biden has attended a dignified transfer ceremony for military members killed in Afghanistan.

The Bidens were joined on the tarmac at Dover by Defense Secretary Lloyd Austin and Gen. Mark Milley, chairman of the Joint Chiefs of Staff. The president and the military leaders stood at attention as the 13 cases, each draped in the U.S. flag were carried one by one out of the bay of C-17 military cargo plane and placed into waiting vans.

As the U.S.-led evacuation effort winds down and tens of thousands of Afghans are left behind, the Biden administration continues to tout an international consensus that the Taliban must provide safe passage out of the country.

“That is a clear expectation across the entire world,” Secretary of State Antony Blinken told ABC “This Week” co-anchor Martha Raddatz.

To back that up, the administration has gotten nearly 100 countries and counting to sign onto another joint statement, saying, “We will continue issuing travel documentation to designated Afghans, and we have the clear expectation of and commitment from the Taliban that they can travel to our respective countries.”

But as Raddatz pressed Blinken, those Taliban commitments mean very little to the Afghan people, particularly those at risk right now because of their U.S. ties or their work for the Afghan government and military.

Blinken conceded that was “certainly” the case, but argued that the international community has “significant leverage to work with over the weeks and months ahead to incentivize the Taliban to make good on its commitments” -- and will also work to keep Kabul airport functioning as soon as possible.

Notably, he also suggested to Raddatz that for the first time there are land routes out of Afghanistan for people to flee -- a dangerous journey that thousands have already had to make, just without the international cameras and attention that there’s been on Kabul and without the guarantees of legal status and safety that these evacuation flights have given so many.

The U.S. has evacuated all Afghan staff who worked at the embassy in Kabul, along with their families, according to an internal situation report obtained by ABC News. It represents 2,800 Afghans in total.

As of 8:30 PM ET Saturday night, there were no evacuees left in the airport awaiting processing, according to the internal report, with the high-level threat preventing U.S. personnel from continuing to process people. It's unclear if that was still the case on Sunday.

"Post continues to receive credible threat reporting of potential terrorist attacks and all gates remained closed," said the report.

Just as the U.S. military begins to draw down its presence, U.S. diplomatic staff are departing now as well, according to the report.

As tens of thousands of Afghan evacuees make their way to the U.S., the report also said some facilities are starting to be overwhelmed. Fort Lee, the U.S. Army post in central Virginia, is near full capacity, while the Dulles airport in northern Virginia has been slow processing arrivals because of the limited security vetting capacity, the report said -- adding it will need to begin flying some evacuees to other locations "to decrease travelers' time in the center, lower total numbers, and allow staff more time for sanitizing and turnover."

-ABC News' Josh Margolin and Conor Finnegan