WATCH: National Security Advisor lays out plans for providing aid to Taliban-led Afghanistan

"Well first of all," Sullivan replied, "we do believe that there is an important dimension of humanitarian assistance that should go directly to the people of Afghanistan. They need help with respect to health and good aid and other forms of subsistence. And we do intend to continue that."

"Secondly," Sullivan said, "when it comes to our economic and development assistance relationship with the Taliban, that will be about the Taliban's actions. It will be about whether they follow through on their commitments: their commitments to safe passage for Americans and Afghan allies; their commitment to not allow Afghanistan to be a base from which terrorists can attack the United States or any other country; their commitments with respect to upholding international obligations. It's going to be up to them and we will wait and see by their actions how we end up responding in terms of the economic and development assistance situation."

During a White House press conference on Tuesday, Press Secretary Jen Psaki said that the Biden administration expects the Taliban to keep their word.

She was asked if she could "clarify if the United States has an agreement with the Taliban to allow more Americans and Afghans to leave the country?"

Psaki replied "It is is our, not just our expectation, but the expectation of 100 countries around the world, the UN Security Council, and others, that the Taliban will abide by what they committed to last Friday, which is the ability of people to leave Afghanistan, should they choose to leave."

"There do need to be ongoing diplomatic negotiations, or discussions, I should say," she said. "That's a part of what the Secretary of State and his team will be leading. But I would not that the Taliban conveyed that on Friday—a leader of the Taliban—again, more than half of the countries in the world have conveyed clearly what they expect, and the UN Security Council signed a resolution yesterday."

"So those are the diplomatic pieces that have moved forward," she said, "but this will be a top priority in the days ahead."

President Biden on Tuesday spoke about the "extraordinary success" the US has seen in Afghanistan, and blamed former President Trump for the situation there when Biden took office. The US first deployed to Afghanistan under President George Bush in the wake of the attacks on New York on September 11, 2001. President Barack Obama reinforced that mission during his two terms in office, for which Biden served as Vice President.