Obama said Wednesday 10,000 U.S. troops would be withdrawn this year and 20,000 more would leave by the end of September 2012.
French President Nicolas Sarkozy said France's phased pullback of the 4,000 soldiers it has contributed to the allied effort would mirror that of the United States.
British Defense Ministry officials said Prime Minister David Cameron's government would consider whether to increase the number of troops it withdraws this year from the 400 originally planned out of a total force of 10,000, The New York Times reported.
Canada, with 3,000 troops, earlier said it would withdraw all its troops this year. Several other European countries already have deadlines for ending their military involvement.
Foreign Minister Guido Westerwelle said Thursday Germany still had to settle on a strategy for its pullback, The Washington Post said.
Afghan President Hamid Karzai praised Obama's withdrawal plan, saying it showed "Afghan forces have become stronger."
"People tell me they now have greater confidence in the security forces," Karzai said at a news conference.
The Taliban, which ruled Afghanistan and provided sanctuary to al-Qaida before the 2001 U.S.-led invasion, dismissed Obama's speech and said "our armed struggle will increase from day to day" until the international coalition is gone, the Post said.