The Taliban were still tightening their grip on's capital city on Wednesday, with the militants controlling access to Kabul's airport. While U.S. nationals have reported being unable to get to the runway for scheduled evacuation flights, those flights were continuing to take off, carrying Western diplomats, workers and their families — and Afghans who've helped them — out of the country.
Note: This article includes an image of injured children which some readers may find distressing.
CBS News correspondent Roxana Saberi and her team were among those who got out overnight on a U.S. cargo plane that brought them to Doha, Qatar, in the Persian Gulf. She and her crew were on the plane with about 300 Afghans who fled the Taliban, most carrying little but hope, and relief.
"If they found me, they're going to kill me," Sayed Jalal-Zaheer told Saberi on the plane. He said he worked as a translator for the U.S. Army, and he had just got hold of U.S. visas for himself and his family.
They left behind thousands of fellow Afghans so desperate to escape that hundreds stormed the Hamid Karzai International Airport runway on Monday, with some clinging to a U.S. military plane as it took off. Amid the chaos, the U.S. military shut down the facility for hours. When limited flights resumed, Saberi and her team headed for the airport.
Inside, they saw some of the roughly 4,000 U.S. troops preparing to airlift thousands of U.S. nationals and Afghans out, and just after midnight local time, they joined them, taking off in the American military transport plane with Afghan men, women and children whom the U.S. is helping to flee from the Taliban.
Back in Kabul, the crush to escape continued on Wednesday. A NATO security official told the Reuters news agency that 17 people were injured in a stampede at a gate to the airport as the U.S. and other Western nations ramped up evacuation efforts, facilitated by an expansion of flight clearance for a limited number of civilian aircraft.
The Taliban has deployed a significant force around the airport and warned Afghans without passports and travel documents not to show up. They used guns and sticks to beat people as they tried to control crowds outside the airport, but the group has promised not to harm anyone who tries to get out of the country.
As many as 10,000 U.S. nationals and their family members are still in Afghanistan. CBS News' Christina Ruffini received messages on Tuesday from one family who said they'd received an email from the U.S. government telling them to go to the airport for evacuation, but when they tried, they encountered gunfire and chaos and headed back to their home to hunker down.
Ruffini pressed State Department spokesman Ned Price on Tuesday to explain what the government was doing to ensure American nationals were able to evacuate.
Price said the U.S. government was, "doing everything within our power to effect a passage, effect a corridor of safe passage for civilians. Of course, that includes American citizens" and Afghans referred for U.S. visas.
"We are going to continue to do all we can," Price said, stressing that it was "a fluid security environment" and adding that if the U.S. was "in a position to do more, I can guarantee you we will do as much as we can."
On Wednesday, Price said more than 1,000 people, including 330 U.S. citizens and permanent residents, were evacuated from Kabul on U.S. military flights over the previous day.
"We have evacuated more than 3,000 people so far, including our personnel," he said. "Additionally, as we have said, we have relocated nearly 2,000 Afghan special immigrants to the United States."
On Tuesday he urged U.S. nationals still in the country to travel to the airport only after receiving notification of a place on an evacuation flight, and even then: "If they feel that it is unsafe for them to make their way to the airport, they should not seek to do so."
CBS News learned later on Wednesday that the State Department was trying to optimize its outreach to American citizens and others in Afghanistan based on the experience of the past several days. U.S. officials were grappling with how to strike a balance to ensure as many available spaces were filled on the evacuation flights as possible, without drawing even larger crowds to the airport gates.
But the clock may be ticking. President Biden has set August 31 as the deadline to get all U.S. forces out of Afghanistan, and it was unclear on Wednesday whether mounting pressure from a group of bipartisan lawmakers would convince the administration to extend that date until the thousands of American troops facilitating evacuations from Kabul had completed the task.
In what seemed like a charm offensive, meanwhile, Taliban spokesman Suhail Shaheen said on Tuesday, in his first-ever televised news conference, that in addition to letting people leave the country, the Taliban would respect women's rights — within the parameters of Islamic Sharia law — and would not take revenge on former enemies.
"I don't believe them," Jalal-Zaheer told Saberi.
He said that if his children and other kids who were on the plane with him Tuesday night ever see Afghanistan again, he hopes it will be with the country at peace, and without the Taliban in power.
CBSNews.com's Tucker Reals contributed to this report.
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