The Taliban has assured the United States it will provide safe passage for civilians to reach the Kabul Hamid Karzai International Airport in Afghanistan, the American national security adviser Jake Sullivan said Tuesday.

Sullivan also told a White House news briefing the U.S. believes the Kabul evacuation can go on until Aug. 31 and it is talking to the Taliban about the exact timeline and how it will play out.

The Taliban declared the war in Afghanistan over after taking control of the presidential palace in Kabul, while Western nations scrambled Monday to evacuate their citizens amid chaos at Kabul airport as frantic Afghans searched for a way out.

Afghan President Ashraf Ghani said Sunday, "The Taliban have won with the judgment of their swords and guns, and are now responsible for the honor, property and self-preservation of their countrymen," after fleeing the country as the militants entered the capital virtually unopposed, saying he wanted to avoid bloodshed. The ensuing hours saw hundreds of Afghans desperate to leave flood Kabul airport.

"Today is a great day for the Afghan people and the mujahideen. They have witnessed the fruits of their efforts and their sacrifices for 20 years," Mohammad Naeem, the spokesperson for the Taliban's political office, told Qatar-based media outlet Al-Jazeera TV. "Thanks to God, the war is over in the country," he said.

It took the Taliban just over a week to seize control of the country after a lightning sweep that ended in Kabul as government forces, trained for two decades and equipped by the U.S. and others at a cost of billions of dollars, melted away.