Around 16,000 troops from U.S., North Atlantic Treaty Organisation and other partner countries are in Afghanistan, training the Afghan forces within the framework of a NATO-led mission.
Maciel was killed and two other American service members were wounded in what U.S. military officials called an "apparent insider attack" on July 7 while they were advising local forces at an Afghan military facility in the town of Tarin Kowt in Uruzgan Province.
The last insider attack occurred in August 2017.
That information could not be immediately verified by Afghan or North Atlantic Treaty Organisation officials.
Pompeo said the proposed talks would be Afghan-led, with the USA playing a supporting role.
The two wounded U.S. service members were not identified but were in "stable" condition on Saturday and are being treated, it added.
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"The wounded service members, who are in stable condition, are now being treated".
The Taliban did not claim responsibility for the attack, but acknowledged it in a message on its official Telegram channel.
The injured American troopers were in stable condition, the statement added. But as NPR's David Welna reported last week, a "public information blackout" by the Trump administration has meant that, "since late previous year, the Pentagon's stopped posting those numbers for Iraq, Syria and Afghanistan".
The names of the service members will not be released until their next of kin were notified. A Pentagon report last month said there were 47 so-called "green-on-green" attacks, or incidents where Afghan soldiers turn on their own side, so far this year.
The last insider attack that resulted in a United States casualty occurred in June a year ago.