Navy Capt Jeff Davis confirmed the deaths. There was no information on the number of troops wounded.
The Taliban quickly took responsibility for the attack, and a spokesman for the insurgents said the bombing allegedly killed 15 soldiers but the Taliban routinely exaggerate their claim and casualty figures.
In their claim of responsibility, the Taliban also said the attack destroyed two armored tanks. The insurgents' spokesman for southern Afghanistan, Qari Yusuf Ahmadi, said fighter Asadullah Kandahari was the "hero" who carried out the attack with a small pick-up truck, packed with explosives.
The service members were part of an international force referred to as the Train, Advise and Assist Command south, a reference to their location in the country.
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Eyewitness Ghulam Ali, who runs a mechanics shop near the attack site on the outskirts of the city of Kandahar, said the intensity of the blast knocked him out.
When he came to, he saw a military vehicle on fire on the road. He stepped out of his shop but a sudden burst of gunfire drove him back inside, he said.
Shah Agha Popal, who runs a vehicle parts shop also nearby, said he also saw soldiers being taken away by two helicopters.
"But I couldn't tell if they were wounded or if they were dead," he said.
The combined US and NATO troop contingent currently in Afghanistan is about 13,500.
The Trump administration is deciding whether to send about 4,000 or more US soldiers to Afghanistan in an attempt to stem Taliban gains.
The attack came as Afghan authorities in western Herat province tightened security ahead of a mass funeral for the victims there of an attack the previous evening that killed 32, said provincial governor's spokesman Jilani Farhad.
The Islamic State group claimed responsibility for the mosque bombing saying it was carried out by two of its fighters. IS said in a statement that the two men, whom it identified as Amir Qassim and Tayeb al-Kharasani, also used automatic rifles in the Shiite mosque before they detonated themselves.
The statement claimed that the attack killed nearly 50 and wounded more than 80.
On Monday, after taking credit for an attack on the Iraq Embassy in the heart of the Afghan capital Kabul, the Islamic State group affiliate in Afghanistan warned it would strike Shiites. The Sunni militant group considers Shiite Muslims as apostates.
Also today the Taliban ambushed and killed Jaghatu District Gov. Manzur Hussain and a passenger in his car, Ghazni provincial police chief Mohammad Mustafa Mayar said. The Taliban have stepped up their attacks in recent weeks hitting district headquarters, government officials and Afghan National Security Forces with increasing frequency.
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