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The militants, now firmly in control of Afghanistan, have “made public and private commitments to provide and permit safe passage for Americans, for third-country nationals and Afghans at risk going forward, past August 31," Mr Blinken said.
“There is no deadline on our work to help remaining Americans and Afghans who helped us. That effort will continue every day after August 31," Mr Blinken said.
Asked about the Taliban's trustworthiness, Mr Blinken said they have a "very strong self-interest in acting with a modicum of responsibility, but they will make their own determination".
He spoke of incentives and leverage the US has as it determines its future relationship with the group.
“If a future government upholds the basic rights of the Afghan people, if it makes good on its commitments to ensure that Afghanistan cannot be used as a launching pad for terrorist attacks directed against us and our allies and partners … that's a government we can work with,” he said.
But if the Taliban choose a different path, "we will make sure that we use every appropriate tool at our disposal to isolate that government. And as I said before, Afghanistan will be a pariah," he added.
The US is racing to fly as many Americans and Afghan allies out of Kabul before the August 31 deadline.
In the past 24 hours, the Pentagon said 19,000 people have left on 90 military cargo aircraft flights.
More than 82,000 Americans, Afghans and other nationals have been flown out of the country, making it the largest airlift in US history.
Since they marched on Kabul on August 14 and 15, the Taliban have been in control of who can approach the perimeter of Hamid Karzai International Airport.
They generally have allowed US passport holders through, although some US citizens have been unable to reach the airport and have had to be rescued by US special forces.
CIA director William Burns flew to Afghanistan this week and held a secret meeting with the Taliban's de facto leader, Abdul Ghani Baradar.
On Tuesday, US President Joe Biden said his administration is on track to finish its evacuation of Afghanistan by August 31. Mr Biden has resisted European and congressional calls to extend the deadline.