Initial reports indicate the attacker was a member of the Afghan National Defense and Security Forces, U.S. Forces-Afghanistan said in a statement Saturday morning.
It said initial reports indicate other Afghan Forces killed the attacker.
The ANSF has been fighting alongside the United States and other Western countries in their effort to assert government control over Afghanistan.
A GoFundMe page has been set up for Taylor's family.
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The unexpected death of Taylor, who was months from finishing his tour and is survived by seven children and his wife Jennie, drew an outpouring of grief in Utah and on social media late Saturday.
When he was ordered to deploy to Afghanistan in January, he announced that he would take a one year leave of absence as mayor.
The two U.S. service members were medically evacuated to Bagram Airfield and the wounded service member was undergoing medical treatment and is in stable condition.
Taylor, who is a member of the Utah National Guard, was elected as mayor of North Ogden (population 17,357) in 2013, and re-elected in 2017, according to Deseret News. Gen. Jefferson S. Burton. "I wish them all the comfort and courage to face the hard days ahead". "We must rally around his family", he added.
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Taylor was a member of an advisory team that was training members of the Afghan commado team on combat operations.
"Things are going great, and I absolutely love the dedicated USA and Afghan soldiers I serve with every day", Taylor wrote in an update about his deployment earlier this year. The image above was posted last week.
His last Facebook post, on October 28, highlighted a successful election in Afghanistan.
Total civilian deaths across Afghanistan - due to various violent attacks - stood at 2,798 for the first nine months of 2018, slightly up from the same period a year ago, according to the United Nations. "Things are going great, and I absolutely love the dedicated U.S. and Afghan soldiers I serve with every day".
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Her daughter Apple is also seen in the top right corner, looking on at her mom and stepdad. Later in the evening, the stunning bride changed into a caped dress by Stella McCartney.
"As the US gets ready to vote in our own election next week, I hope everyone back home exercises their precious right to vote", Taylor wrote.