One American service member was killed and two others were wounded on Saturday in what the USA -led coalition described as an "apparent insider attack".
Pompeo said the proposed talks would be Afghan-led, with the US playing a supporting role.
The incident is being investigated.
There were 47 "green-on-green" attacks, when Afghan security forces are attacked from within their own forces, from December 1, 2017 through May 31.
A statement issued by the Resolute Support Mission on Saturday said two other USA service members were wounded but in a stable condition.
Alliance officials said the two wounded service members were in stable condition and receiving medical treatment.More news: Colombia suffered 'monumental theft' against England, claims Maradona
Maciel's task force was deployed in support of the 1st Security Force Assistance Brigade, a newly established unit that is focused on advising and bolstering local troops and is seen as critical to America's strategy in Afghanistan.
Afghan President Ashraf Ghani had extended a recent holiday cease-fire in hopes of encouraging the militants to come to the bargaining table, but the Taliban rejected the offer and resumed attacks.
Pompeo said the US will "support, facilitate, and participate in these discussions", but emphasized negotiations with the Taliban must be "Afghan-led and Afghan-owned".
The war in Afghanistan has gone on for 17 years.
Insider attacks on Afghan forces - and deaths resulting from those attacks - have increased by more than 50 percent compared to the same time frame past year. A U.S. Defense Department report released earlier this month found civilian casualties had increased 73 percent between December and May compared to the same period the year before.