Britain has already offered an extra 500 and Prime Minister Gordon Brown said they would be accompanied by new forces from at least eight other NATO allies, as well as the United States.
Italy has said it will send an unspecified number, while Poland is considering deploying several hundred more soldiers.
French President Nicolas Sarkozy said he "provides his full support" for Obama's strategy and called "on all countries which want to help the Afghan people to support it," but said France would wait until an international conference on Afghanistan on January 28 to review its troop contribution.
Sarkozy said France expects to hear at the conference clear commitments from Afghan leaders on a range of issues including taking over responsibility for security, which will allow the international community to review its efforts.
German Chancellor Angela Merkel said her country would also wait until after the London conference.
"After this conference on Afghanistan, Germany will decide whether or not it will make fresh efforts, and if so, what efforts," Merkel said, adding that security in Afghanistan would not be solved by military means alone.
Germany has around 4,300 troops in northern Afghanistan, the third largest contributor to a 100,000-strong international force after the United States and Britain, whose extra 500 troops will take it past 10,000.
Brown set three conditions for Britain sending extra troops to Afghanistan.
These were that the Afghan government show a commitment to providing police and soldiers who can be trained to engage in combat; that British troops are properly equipped and that other NATO countries also boost force levels.
Polish Prime Minister Donald Tusk said after a telephone call from Obama that his country could beef up its contingent of 2,000 troops by several hundred.
"According to President Obama, a bigger engagement (now) could allow for starting to withdraw the forces in 18 to 24 months from now at the latest," Tusk said Tuesday.
Australian Prime Minister Kevin Rudd pledged Monday to send more police trainers and civilian aid experts, saying his country was in it "for the long haul."
But Rudd, who met Obama in Washington this week, did not offer more troops beyond the 1,550 that Australia has already committed.
His Defence Minister John Faulkner said he hoped the increase in US troops would make a "significant difference" on the ground, while reiterating: "We're not planning to send additional troops to Afghanistan".
Washington: NATO foreign ministers will be meeting in Brussels on Friday to discuss Afghanistan, where more than 40 countries have troops.
First Published: Wednesday, December 02, 2009, 17:38