The military held a news conference on Saturday to release the findings of an inquiry into TV footage last month that showed US soldiers using the cremation to taunt other insurgents - an act that sparked outrage in Afghanistan.
Islam forbids cremation, and the video images were compared to photographs of US troops abusing prisoners at Iraq's Abu Ghraib prison.
The US-led coalition's operational commander, Major-General Jason Kamiya, said two junior officers who ordered the burning of the bodies would be officially reprimanded for showing a lack of cultural and religious understanding; but he added the men were unaware that what they were doing was wrong.
Kamiya also said two non-commissioned officers would be reprimanded for using loudspeakers to taunt Taliban insurgents who were believed to be lingering in a nearby village after a clash with the US troops.
"Our investigation found there was no intent to desecrate the remains, but only to dispose of them for hygienic reasons"
Major-General Jason Kamiya, US-led coalition's commander
The two men would also face non-judicial punishments, which could include a loss of pay or demotion in rank.
No desecration intent
"Our investigation found there was no intent to desecrate the remains, but only to dispose of them for hygienic reasons," Kamiya said.
He added that the broadcasts, while "designed to incite fleeing Taliban to fight", violated military policy.
The video footage threatens to undermine public support for the US military's war against a stubborn insurgency four years after US-led forces ousted the Taliban government.
Hours after it was broadcast in Australia last month, American commanders scrambled to contain the public relations fallout, promising a full investigation and vowing that anyone found guilty would be punished to the full extent of military law.
Saturday's news conference was held in the former Taliban stronghold of Kandahar, the closest city to where the alleged desecration occurred on 1 October.
It was attended by Kandahar Governor Asadullah Khalid, who said afterwards: "We have confidence in this investigation."
The TV footage showed five soldiers in light-coloured military fatigues, which did not have any distinguishing marks, standing near a bonfire in which two bodies were laid side by side.
Kamiya said the temperature at the time was 33C and that the bodies had lain exposed on the ground for 24 hours and had begun to rapidly decompose.
"This posed an increasing health concern for our soldiers," Kamiya said. "The criminal investigation proved there was no violation of the rules of war."
The Geneva Convention forbids the burning of combatants except for hygienic purposes.
Afghan President Hamid Karzai
ordered his own inquiry
The bodies were found atop a hill following a firefight, and Kamiya said soldiers, intending to stay on the hill for two or three days for strategic reasons, thought other Taliban had fled into the village below.
Afghan President Hamid Karzai ordered his own inquiry into the incident. That investigation has been completed, but officials say it is not known when its findings will be released.
Swedish soldier dies
A Swedish soldier died from injuries suffered in a roadside bomb blast on Friday, and suspected Taliban insurgents burned down a district police headquarters and abducted four officers in a pre-dawn attack on Saturday.
One of four Swedish soldiers who were wounded on Friday when a bomb tore through a vehicle carrying peacekeepers in the northern city of Mazar-e-Sharif later died, the Swedish military and the Nato-led International Security Assistance Force said.
Another soldier was in "very serious" condition, while the other two suffered minor injuries, the Swedish Armed Forces said in a statement. Two civilians were injured in the attack as well, officials in Afghanistan said.
Before sunrise on Saturday, insurgents attacked a district police office in Logar province near the capital, burning it down and abducting four officers, provincial deputy police chief Abdul Rasool said.
The attack sparked a gun battle, but police suffered no casualties and it was unknown whether any fighters were wounded or killed, Rasool said.
"We suspect that they wanted to explode these cars in the city"
Mohammed Zahir Azimi, Afghan
Defence Ministry spokesman
He said the assailants fled after the authorities dispatched soldiers to the area, and that security forces were searching for the insurgents and the missing policemen.
Also on Saturday, the authorities in Kabul seized two explosive-laden vehicles and arrested six Afghan men on suspicion of planning attacks, Defence Ministry spokesman General Mohammed Zahir Azimi said in a statement.
"We suspect that they wanted to explode these cars in the city," he said without giving any further details.