The soldiers were training Afghan forces, he said.
Two more Americans were killed in a roadside blast in southern Afghanistan, Naranjo said.
And another American soldier died of wounds sustained during a firefight with fighters in the east, a US military spokesman said.
It was the deadliest day for American troops in Afghanistan since July 13, 2008, when 10 soldiers were killed.
Separately, the Taliban claimed on a website that they were holding an American soldier who the US military says fighters might have captured last week.
The Taliban statement, however, did not include any proof, such as a picture or the soldier’s name.
Earlier on Monday, a suicide car bomber blew himself up outside the outer gate of the main Nato base in the southern Kandahar province, killing two civilians and wounding 14 other people.
Those wounded near the gates of Kandahar airfield included 12 civilians and two Afghan soldiers, General Sher Mohammad Zazai, the military commander for southern Afghanistan, said.
The developments came as Barack Obama, the US president, said it was too soon to measure the success of his new strategy in Afghanistan.
He said the US can take another look at the situation after the country’s presidential elections on August 20.
Obama has ordered 21,000 additional American troops to this country, mainly in the south where Taliban fighters have made a violent comeback after a US-led multinational force topped them from power in late 2001.
The US expects 68,000 troops in Afghanistan by year’s end, double last year’s total but still half as many as now in Iraq.
About 4,000 US marines, backed by a 650-strong force of Aghan security personnel, began an offensive – dubbed Operation Strike of the Sword – on Thursday in the southern Helmand province.
The operation is aimed at seizing control of areas in the lower Helmand valley and then securing them with US, Nato or Afghan forces.
About 500 marines moved into the Khan Neshin area on Monday, according to a military statement.
“This is the first time coalition forces have had a sustained presence so far south in the Helmand River valley,” it said.
“Khan Neshin had been a Taliban stronghold for several years before Afghan and coalition forces arrived and began discussions with local leaders several days ago.”