The current conflict began in 2001 with the US -led invasion to unseat the Taliban and hunt down al-Qaeda leader Osama Bin Laden.
The discrepancy between the number of fatalities given by the U.S. and the Taliban could not immediately be explained, but the Taliban often exaggerates its claims.
He said the attackers opened fire at guests inside the hotel.
Officials said two of the gunmen were killed and one suspect had yet to be apprehended.
"The name of the service member killed in action is being withheld until 24 hours after notification of next of kin is complete", Resolute Support, the US-led North Atlantic Treaty Organisation mission in Afghanistan, said in a statement.
Separately, Afghanistan's Islamic State affiliate claimed Friday's suicide attack that killed 6 people.
The killings occurred a day after U.S. Secretary of State Mike Pompeo made a quick visit to the Afghan capital of Kabul where he said Washington was hopeful of a peace deal before September 1.
PHOTO: In this photo taken on June 6, 2019, USA soldiers look out over hillsides during a visit of the commander of US and North Atlantic Treaty Organisation forces in Afghanistan Gen. Scott Miller at the Afghan National Army (ANA) checkpoint in Nerkh district of Wardak province.
Saturday's announcement brings the total number of USA troop deaths in Afghanistan this year to 11, according to iCasualties, a website that tracks casualties of US forces in Afghanistan and Iraq.
The U.S. top negotiator Zalmay Khalilzad described the recent discussions as "the most productive session to date".
The event comes days after the seventh round of talks between USA and Taliban representatives concluded in Doha, Qatar, which focused on the withdrawal of US troops and a permanent cease-fire. The United States does not use tanks in Afghanistan.