The US forces are part of the Nato-led Resolute Support Mission in Afghanistan, which has more than 16,000 personnel.
The three service members' deaths bring the total American deaths in Afghanistan for the month of November to five.
US special operations troops often accompany their Afghan counterparts into battle as part of a joint counterterrorism mission, which is separate from the much larger USA and coalition mission to train and equip government forces battling a 17-year Taliban insurgency. Last Saturday, Sgt. Leandro Jasso, a 25-year-old Army Ranger from Leavenworth, Washington, was mortally wounded in southern Afghanistan.
One American contractor was also injured.
The military later said that Jasso was likely killed by friendly fire from partner Afghan forces after they engaged in a "close-quarter battle" during an assault on one of the multiple barricaded al-Qaeda shooters.
The NATO statement gave no details but Mohammad Arif Noori, a spokesman for the provincial governor, said an armoured vehicle carrying United States troops hit a large roadside bomb in Shahbaz area, just outside the city on Tuesday morning. Insurgent influence or control has risen to 12.5% of districts from just 7%, and approximately a third of Afghanistan is a "contested" area.
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The Taliban have an active presence in Ghazni province and tried to take over the capital in August. The two districts, which are predominantly comprised of Hazara populations, were considered to be the most secure rural districts in all of the country.
The Taliban claimed responsibility for the attack, AFP reported.
The Taliban routinely reports on its operations in Ghazni on its official propaganda website.
The violence comes as the Taliban intensifies pressure on Afghan security forces, even as the global community ramps up efforts towards talks.
Within the package, €311m is allocated to support the Afghan government in pursuing its reform agenda, €80 million to improve the health and nutrition of the population, and €15.5m will support the presidential and provincial council elections in 2019.