General Hank Taylor, Deputy Director of Logistics for the US Joint Chiefs of Staff, acknowledged that they have operated without "hostile interactions, attacks or threats" by insurgent forces.
The United States reported an acceleration in the pace of evacuations from Afghanistan on Tuesday, noting that the Taliban who control Kabul were not disrupting operations at the airport.
A senior official of the Pentagon's Joint Chiefs of Staff reported that the US military at the air terminal had contacted the commanders of the Taliban forces and that they were confident that the departure of thousands of US and Afghan citizens on US military aircraft would continue in the coming days.
"We have not had any hostile talks, no attacks or threats from the Taliban," General Hank Taylor told reporters.
Taylor said that since the Kabul airport reopened early Tuesday after a several-hour shut down due to security concerns, the United States has evacuated about 800 people, including 165 Americans, on seven flights.
The US Defense Department has sent troops to the Kabul airport since Saturday to protect people's escape after the Taliban regained power after a lightning offensive.
Taylor said the number of US troops would rise from 2,500 on Monday to around 4,000 on Tuesday night.
The goal of the United States, he said, is to increase flights to one plane per hour to transport between 5,000 and 9,000 passengers per day. "We have taken appropriate steps to resume safe and orderly operations at the airport," he said.
Other countries, including Germany and France, have also managed to land planes in Kabul to pick up their eligible Afghans and citizens.
Taylor spoke a day after images of hundreds of Afghans circulated on the Kabul airport runway trying to prevent the departure of a substantial C-17 heavy military transport plane by clinging to the outside of the aircraft.
The videos appeared to show two people falling from the plane after it took off. Another, according to the Washington Post, was later found dead in the landing gear.
Pentagon spokesman John Kirby said the US Air Force was investigating those incidents.
Taylor did not provide figures on how many US citizens, Afghans, or other nationals were currently at the Kabul airport trying to leave the country.
The United States has pledged to accept tens of thousands of people who worked for US forces and their families, who fear retaliation from the Taliban.
"The Taliban have informed us that they are willing to provide a safe passage for civilians to the airport, and we intend to implement that commitment," National Security Adviser Jake Sullivan told reporters at the White House.
Sullivan said the United States was also " talking " to the Taliban about the timetable for the transfer of American and Afghan civilians.
The National Security Advisor maintained that President Joe Biden has not spoken to any international leader since Kabul fell to the Taliban: "He has not yet spoken to any other world leader."
"Myself, Secretary (Antony) Blinken, several other senior members of the team have been engaged regularly with foreign counterparts, and we intend to do so in the coming days, " he added.