At least 15 people were killed on Tuesday in two separate attacks by militants in Afghanistan as Islamic scholars gather in Saudi Arabia to discuss the legitimacy of the Taliban's war against the USA -backed government of President Ashraf Ghani.
Pompeo said there now is hope for progress - with an increase in airstrikes and the deployment of an additional 3,000 USA troops.
This war started 17 years ago when Americans Invaded Afghanistan and thus Afghan Mujahid nationals launched the jihad, the group said.
The Taliban released a statement praising an Afghan soldier for carrying out the attack, without taking credit for it themselves.
Additional information will be released as appropriate, the statement added.
As well as the battle against the Taliban and Islamic State fighters operating from Afghanistan, Pompeo discussed plans for October elections in the country and presidential elections due early next year, amid tensions between powerful regional leaders and Ghani. Afghan commandos carried out the operation with support from US special forces and air power.
"Green on blue" attacks, where Afghan soldiers or those purporting to be Afghan soldiers attack troops from the US and its North Atlantic Treaty Organisation partners, have occurred regularly in the long-running way, as have "green on green" attacks of Afghan soldiers turning against their comrades.