He said the strategy announced a year ago by President Donald Trump of sending more troops to increase pressure on the Taliban and push them toward negotiations was working, and would reassure Afghans "that we will support them as they continue fighting to liberate their country and their people".
"An element of the progress is the capacity that we now have to believe that there is help, that numerous Taliban now see that they can't win on the ground militarily", stated the secretary of state.
"An American role will be important in this, but we can't run the peace talks, we can't settle this from the outside", Pompeo said, according to a transcript of his remarks.
The attack comes a year after three U.S. special forces soldiers were shot dead by one of their Afghan colleagues.
The US would "continue to welcome any partner who supports a Kabul-led peace process without further destabilising Afghanistan", it added.
The ceasefire initiative prompted the insurgent group to announce its own cessation of hostilities during the three-day Eid festival. Two other Americans were wounded in the attack.
Insider attacks on Afghan forces - and deaths resulting from those attacks - have increased by more than 50 percent compared to the same time frame a year ago.
The US still has an estimated 14,000 troops in the country helping support the Afghan military, despite NATO's combat mission in Afghanistan officially ended in 2014.
"The Afghan Mujahid nation does not expect authorities of Saudi Arabia and scholars to side with American invaders in this fight between Islam and disbelievers", the Taliban said in a statement. "And we would like to see those steps extended to more vigorous counterterrorism effort on behalf of the Pakistani government".