The drawdown is the first step in a plan to transfer the country's security completely to Afghan forces by 2014.
An Afghan presidential press office statement said Karzai thanked Obama for Wednesday's address on the troop reduction, saying the Afghan people had suffered much during last three decades of ongoing conflict, the Wakht News Agency reported.
Karzai said the troop drawdown was in the interest of both countries and he supports the process, Wakht reported. The drawdown would leave about 68,000 troops in place.
The Afghan president said Afghan forces would fill the vacuum left by departing U.S. troops, despite widespread fears the withdrawal could trigger an intensification of the conflict, the Financial Times reported.
CNN reported Karzai said Afghans are "happy" with the process.
"The number of troops that he has announced to be withdrawn is a sign that Afghanistan is taking over its own security and is trying to defend its territory by its own means," Karzai said. "So we are happy about the announcement."
He said Afghanistan can look forward to a more stable future, despite the fact that May was the bloodiest month for Afghan civilians since 2007. He told CNN's Fareed Zakaria in an interview set to air Sunday that Afghans were ready to take the reins of their own country.
"It is the responsibility of the Afghan people to protect their country and to provide security for the citizens of the country," Karzai said. "If you fail in fulfilling our most important responsibility with regard to our country and our people, then somebody else should take over."
Karzai also defended his sometimes angry public criticisms of NATO in recent weeks, CNN reported, saying his comment on NATO becoming an "occupying force" was taken out of context.