ABC News' Luis Martinez pressed Pentagon press secretary John Kirby at a briefing on Thursday on whether there's been progress getting people access to the airport in Kabul.

While Kirby said the Pentagon is "hopeful" for a more consistent increase in the flow of people in the coming days, he said, "I can't tell you right as we speak here, Louis, that there's been some dramatic rise."

“We've got additional consular officers now at the additional gates with additional troops helping the consular officers. And so I think we're poised to see an increase, but I want to be careful before I make predictions," he added.

The U.S. has evacuated 7,000 people from Kabul since Saturday but hopes to have the capacity to evacuate 6,000 to 9,000 a day, officials said. In the last 24 hours, 2,000 evacuees were airlifted out as getting evacuees safely to the airport and processing them to be let inside and onto flights remains the greatest hurdle for officials.

"It's not about the math, it's about what's ready to fly, who's on the airfield, ready to leave a holding area and get on the aircraft, and as those numbers increased, which you've seen they have in the last 24-48, the CENTCOM command team will continue to bring in the airflow required to fly out those people,” said Maj. Gen. Hank Taylor.

Kirby went on to list some of the choke points the U.S. is still facing.

"There are lots of factors that go into the throughput, including the situation out in town, including the checkpoints that the Taliban have set up, including processing at the gates where we have set up,” he said. “Weather is a factor, and of course security at the airport is a factor.”

At a briefing on Thursday, Pentagon officials addressed the military's use of armed F-18 overwatch flights above Kabul, saying the planes are there to ensure “close air support” if needed.

“There had been some reporting out there that we were, you know, flying low passes over the city or some kind of shows of force -- that's not what this is. This is just an added layer of force protection is the prudent and responsible thing to do,” Pentagon press secretary John Kirby said.

While Kirby said the Taliban has agreed to allow Americans to pass through to the airport, he said there’s “no update" on assurances from the Taliban on allowing safe passage for Afghans. He did indicate that there have been signs of progress in terms of vetting Afghans, which helps to get them through.

"We've made it very clear to the Taliban that any attack upon our people or our operations at the airport will be met with a forceful response,” he said. “There's been no hostile interactions between the Taliban and our forces or American citizens.”

Kirby continued, “Now we have seen reports of the Taliban, harassing -- and physically so -- some Afghans that were trying to move to the airport. We are in constant communication with them."

More than 5,200 troops are at the airport in Kabul and multiple gates are now open to "help expedite processing in a safe and orderly manner," said Maj. Gen. Hank Taylor, joint staff deputy director for regional operations.

Maj. Gen. Hank Taylor, joint staff deputy director for regional operations, said from the Pentagon on Thursday that the U.S. has evacuated approximately 7,000 people from Afghanistan since Saturday.

“We're ready to increase throughput and scheduled aircraft departures accordingly. We intend to maximize each plane's capacity," he said. "We're prioritizing people above all else, and we're focused on doing this as safely as possible with absolute urgency."

Taylor said multiple gates into the Hamid Karzai International Airport are now open and that the military has not experienced any security incidents overnight.

"We continue to recognize the inherent danger of operating in this environment, but our service members in Kabul remain agile, professional, in our posture to continue mission and to respond if required.”

With the rapid collapse in Afghanistan leading some veterans of America's longest war to question whether their service there was worth it, Commandant of the U.S. Marine Corps Gen. David Berger and Marine Corps. Srgt. Major Troy Black have sent a message to all Marines telling them, "Yes."

“We both believe – without question – that your service was meaningful, powerful, and important," they said in a a joint letter to U.S. Marines.

They went on to outline U.S. missions that have kept America safe and protected the liberties of Afghan women and men.

“You never let them, down. You never, ever gave up. You lived with purpose, with intention," they said.

In a similar vein, the Pentagon issued a press release Wednesday night listing mental health resources for service members and their families.

“You are not alone. Remember that what is happening now does not minimize or negate the experiences of all who served overseas," the message from the Defense Department said. "Service is never for naught."