Earlier this month, Vice President Joe Biden said in an interview with Newsweek magazine that the Islamist militants did not represent a threat to U.S. interests unless they continued to shelter Al Qaeda.
Biden's comments came amid reports that the Obama administration and other governments are trying to establish a peace process with the Taliban to help end the 10-year war.
"I am very happy that the American government has announced that the Taliban are not their enemies," Karzai said in a speech to the Afghan Academy of Sciences. "We hope that this message will help the Afghans reach peace and stability."
A senior U.S. official has told The Associated Press that Washington plans to continue a series of secret meetings with Taliban representatives in Europe and the Persian Gulf region next year.
The U.S. outreach this year had progressed to the point that there was active discussion of two steps the Taliban seeks as precursors to negotiations, the official said, speaking on condition of anonymity due to the sensitivity of the issue.
Trust-building measures under discussion involve setting up a Taliban headquarters office and the release from the U.S. military prison at Guantanamo Bay, Cuba, of about five Afghan prisoners believed affiliated with the Taliban.
Meanwhile, NATO troops on Saturday handed over responsibility for security in three districts of the embattled southern Helmand province to Afghan forces.
Helmand governor's office said these included Marjah district -- the site of a major offensive by coalition forces last year. Coalition operations to rout the Taliban in February 2010 yielded slower than expected returns, but a troop buildup later in the year pushed insurgents out of the main center of the district.
Nad Ali, which had been run by British troops, also transitioned from NATO to Afghan security control, a statement said.
The handovers in Helmand are part of the second phase in a transition NATO and Karzai hope will leave Afghan forces in control of the entire country by the end of 2014, when the U.S.-led coalition's combat mission is scheduled to end.