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WATCH: Pentagon’s John Kirby and Gen. Steve Lyons hold briefing amid Afghanistan pullout

Commander of U.S. Transportation Command say he takes the evacuation efforts in Afghanistan personally and “will not rest until the mission is complete.”

Watch their remarks in the player above.

Army Gen. Stephen Lyons comments came via video conference at the Pentagon on Monday.

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.

This comes after President Joe Biden said Sunday he would not rule out extending the evacuation beyond August 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.

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.”

Since the Taliban seized the capital Aug. 15, completing a stunning rout of the U.S.-backed Afghan government and military, the U.S. has been carrying out the evacuation in coordination with the Taliban, who have held off on attacking under a 2020 withdrawal deal with the Trump administration.

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.