"And right now, you know, yes, green on blue could be a threat, but we have not had a single incident", Jackson said, using a military term for insider attacks.
Officials said the incident is being investigated, and no further details were immediately available.
Pompeo said the proposed talks would be Afghan-led, with the US playing a supporting role.
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The number of insider attacks peaked at 61 in 2012, but the attacks have become rare after the US military instituted security safeguards to protect American troops.
U.S. Secretary of State Mike Pompeo, right, arrives for a press conference with Afghan President Ashraf Ghani, second right, at the presidential palace in Kabul, Afghanistan, Monday, July 9, 2018. Some of the USA forces are involved in counterterrorism operations, particularly against the Islamic State jihadist group.
The death on Saturday is the third of an American service member in Afghanistan this year, adding to more than 2,200 US troops killed and 20,000 wounded there since the invasion in 2001.
The last insider attack occurred in August of 2017.
The latest incident comes as Lieutenant General Scott Miller is set to become the next commander of US and North Atlantic Treaty Organisation forces in Afghanistan. "The Taliban have gained ground, USA airstrikes have spiked to put pressure on the group to negotiate, and civilian casualties have increased - partly due to those airstrikes but mostly because of Taliban attacks, and some ISIS attacks".