US-led coalition forces say they have killed 32 "enemy fighters", assumed to be the Taleban and their allies in clashes in southern Helmand province.
One US and one Canadian soldier were killed, the US says after a coalition base came under attack.
Five other soldiers, including one American and three Canadians, were wounded in Wednesday's fighting.
The Taleban are reported as saying that they have begun a new spring offensive against foreign and government forces.
Helmand province has been at the centre of a recent upsurge in fighting.
The US military said on Wednesday that coalition forces had "defeated a large enemy element that was attempting to retreat into sanctuaries".
It said 12 militants were killed earlier in the day and another 20 in subsequent fighting.
A US military statement said: "Coalition forces also discovered large caches of munitions as they overran the Taleban compound and the enemy fled. Coalition forces destroyed the munitions."
"With our coalition partners and the government of Afghanistan we are committed to continuing offensive operations against the Taleban and other terrorists that are attempting to disrupt the considerable progress of reconstruction and governance in Afghanistan," Brig Gen Anthony Tata said.
There has been an upsurge of violence in Helmand
The Reuters news agency quoted a man who identified himself as a Taleban spokesman saying they had begun a spring offensive against foreign forces.
"The weather is warming and Taleban attacks on coalition and Afghan forces have begun," a man who called himself Mullah Mohammad Hanif said by telephone from an undisclosed location.
Over 220 US military personnel have been killed in Afghanistan there since the ousting of the Taleban in 2001, according to reports.
More than 3,000 British troops are to be deployed in the province in the coming months.