The U.S. military reported its biggest day of evacuation flights out of Afghanistan by far on Monday, but deadly violence that has blocked many desperate evacuees from entering Kabul's airport persisted, and the Taliban signaled they might soon seek to shut down the evacuation. Twenty-eight U.S. military flights ferried about 10,400 people to safety out of Taliban-held Afghanistan over the 24 hours that ended early Monday morning, President Joe Biden's national security adviser, Jake Sullivan told reporters. "In the days remaining, we believe we have the wherewithal to get out the American citizens who want to leave Kabul," Sullivan insisted. Sullivan said that talks with the Taliban are continuing. "We are in talks with the Taliban on a daily basis through both political and security channels," he said, adding that ultimately it will be Biden's decision alone whether to continue military-led evacuation operations beyond August 31. After more than a week of evacuations plagued by major obstacles, including Taliban forces and crushing crowds that are making approaching the airport difficult and dangerous, the number of people flown out met — and exceeded — U.S. projections for the first time. The count was more than twice the 3,900 flown out in the previous 24 hours on U.S. military planes. "We have developed a method to safely and efficiently transfer groups of American citizens onto the airfield," Sullivan said, but for operational reasons he declined to give details. Biden said Sunday he would not rule out extending the evacuation beyond Aug. 31, the date he had set for completing the withdrawal of troops and formally ending the nearly 20-year U.S. military role in Afghanistan. And British Prime Minister Boris Johnson plans to press Biden for an extension to get out the maximum number of foreigners and Afghan allies possible. Biden is to face the U.S.'s G-7 allies in a virtual summit on Afghanistan Tuesday. But Taliban spokesman Suhail Shaheen, in an interview with Sky News, said that Aug. 31 is a "red line" the U.S. must not cross and that extending the American presence would "provoke a reaction." Monday's warning signaled the Taliban could insist on shutting down the airlifts out of the Kabul airport in just over a week. Lawmakers, refugee groups, veterans' organizations and U.S. allies have said ending the evacuation then could strand countless Afghans and foreigners still hoping for flights out. Biden and his top aides have repeatedly cited their concern that extremist groups in Afghanistan will attempt to exploit the chaos around the Kabul airport. "We are sustaining the highest level of vigilance for an attack against the airport by ISIS-K or another terrorist group," Sullivan said. "Our commanders on the ground have taken every step they can to prepare for such an attack." The Biden administration has given no firm estimate of the number of Americans seeking to leave Afghanistan. Some have put the total between 10,000 and 15.000. Subscribe to our YouTube channel: https://bit.ly/2TwO8Gm Subscribe to our newest channel Quicktake Explained: https://bit.ly/3iERrup Bloomberg Quicktake brings you live global news and original shows spanning business, technology, politics and culture. Make sense of the stories changing your business and your world. To watch complete coverage on Bloomberg Quicktake 24/7, visit http://www.bloomberg.com/qt/live, or watch on Apple TV, Roku, Samsung Smart TV, Fire TV and Android TV on the Bloomberg app. Have a story to tell? Fill out this survey for a chance to have it featured on Bloomberg Quicktake: https://cor.us/surveys/27AF30 Connect with us on… YouTube: https://www.youtube.com/user/Bloomberg Breaking News on YouTube: https://www.youtube.com/c/BloombergQuickTakeNews Twitter: https://twitter.com/quicktake Facebook: https://www.facebook.com/quicktake Instagram: https://www.instagram.com/quicktake