The large operation was launched in the Uzbin Valley, a Taliban stronghold, to give control back to Afghan security forces.
French military officials say more than 1,000 soldiers, including Afghan, U.S. and 800 French legionnaires, have launched a major offensive east of the Afghan capital, Kabul.
Officials say some American soldiers were wounded and some insurgents killed during the fighting, but it was not clear how many. The operation was launched in the Uzbin Valley, a Taliban stronghold where 10 French soldiers were killed in an ambush in 2008. The offensive is aimed at giving control of the area back to Afghan security forces.
U.S. President Barack Obama has ordered 30,000 extra U.S. troops to be deployed in Afghanistan as part of his new strategy to reverse gains by the Taliban-led insurgency in recent years.
Spain's Defense Minister on Thursday announced plans to send an additional 511 soldiers to train Afghan forces, acquiescing to Mr. Obama's request for more help from allied forces. If Spain's parliament approves the measure, it would raise the number of Spanish troops in Afghanistan to a little over 1,500.
Separately, U.S. lawmaker John Teirney launched an investigation into whether U.S. tax money is being used to pay Afghan warlords and militants for protection on supply routes.
Tierney, a Democrat from Massachusetts, says "serious allegations" have arisen that private security companies working with U.S. transportation contractors are regularly paying local warlords and the Taliban. He announced Wednesday that the House National Security and Foreign Affairs subcommittee launched a preliminary inquiry and determined that the reports warrant a "full-scale" investigation.
U.S. Secretary of State Hillary Clinton raised the same issue during testimony before a Senate panel earlier this month. She noted that U.S. supplies are offloaded from ships in Pakistan's port of Karachi, then are trucked to Afghanistan. Clinton said "protection money" paid to ensure the supplies' safe travel is a major source of funding for the Taliban.
Tierney says the U.S. has a more than $2 billion contract with the Afghan Host Nation Trucking, a deal split among eight companies that provide ground transportation in Afghanistan. He says the companies transport more than 90 percent of U.S. defense supplies, including food, fuel and ammunition.
Some information for this report was provided by AP and AFP.