But, Pompeo said, the U.S. will only sign an agreement with the militant group to withdraw American troops if that reduction holds until Saturday and is declared a success.
The U.S. announced a deal with the Taliban and Afghan government last Friday to reduce violence for seven days, starting at midnight local time. While the Taliban claimed Saturday that it allowed them to still attack Afghan security forces, the U.S. and Afghan government -- which the Taliban refuses to recognize -- said it included Afghan troops and extended nationwide.
Since then, the truce has largely held, according to Pompeo: "It isn't perfect, but it's working," he told reporters Tuesday.
"If -- and only if -- it's successful," he added, the chief U.S. negotiator Zalmay Khalilzad and senior Taliban officials will sign a deal on Saturday that means the beginning of a "conditions-based and phased" U.S. withdrawal and the "commencement" of Afghan negotiations where "all sides of the conflict will sit down together and begin the hard work of reconciliation."
In particular, Pompeo was pressed Tuesday on whether the U.S. is committed to ensuring women's rights are defended in a future Afghan government. But he said that would be up to Afghan negotiators to decide, signaling it is not an explicit part of any U.S.-Taliban agreement.
"Our mission set there has been much broader than that," he said, latter adding "the Afghans will drive the solution."
The U.S. will assist those talks, providing structure and support along with other countries like Germany and Norway, he said.
The talks will bring together a Taliban delegation with other Afghan leaders, including tribal chiefs and members of the government. But because the Taliban rejects the government, those officials will have to participate in a "personal" capacity, even after being chosen by President Ashraf Ghani's administration.
Instead of guaranteeing any particular outcome from those talks, Pompeo made clear the phased U.S. withdrawal will depend only on the Taliban's commitments to the U.S. -- sitting for those negotiations in the first place and, perhaps more importantly to the administration, severing ties to terrorist groups.
"We're not required to leave unless they can demonstrate they are fulfilling every element of their end of the bargain," he said. "Our conditions-based withdrawal sets a high bar for the things that will take place in order for America to ensure that we can accomplish both of those missions" -- peace and reconciliation among Afghans and keeping the U.S. homeland safe, he added.
While Pompeo said he was "very confident" that women's rights "will be addressed as part of these conversations," the withdrawal of U.S. forces doesn't seem contingent upon it -- and that's what has women's rights advocates most concerned.
"What we Afghan women fear is that this situation will get worse after international forces withdraw from Afghanistan next year. We fear we will lose our rights and security, particularly if the Taliban are brought back into government," according to Tamana Heela, an Afghan women's rights activist. "Afghan women need continued international support to ensure that doesn't happen."
It's a message that Afghan women have tried to press upon Khalilzad -- the former U.S. ambassador to Afghanistan, Iraq and the United Nations -- during his year and a half of negotiations with the Taliban.
The Taliban have been "calling the shots," Mahbouba Seraj, a women's rights activist, told ABC News last June. "They want to get anything and everything the way they want to. Amongst them, of course, is our freedom, whatever we have so far and what we have worked so hard with the help of the world to get for the last 18, 19 years."
A State Department official told ABC News at the time that U.S. negotiators "assert that civil rights must be protected in any peace agreement, and that women must be an integral part of intra-Afghan dialogue and negotiations."
They have also made clear that any future relations with the U.S. and the rest of the international community "will rest in part on what [Afghanistan] does to maintain the civil rights of women," the official added.
But Pompeo has also stressed since last spring that it is the role of Afghan women to speak up and demand equality -- an act that has gotten many, including Heela's mother, killed.
"I hope the women of Afghanistan will demand that of their leaders," he told Sen. Jeanne Shaheen, D-N.H., in April. "We've always done our part there."