Brown's confirmation of an earlier, conditional pledge comes a day before U.S. President Barack Obama is expected to announce 30,000 more troops to fight the Taliban and train Afghans so that foreign forces can eventually be withdrawn.
I believe over the coming months even more countries will respond, Brown told parliament.
A spike in casualties in the eight-year war against the Taliban has forced NATO military chiefs to rethink their strategy and call for more troops to stabilize conditions after presidential elections this year.
A British soldier was killed by an explosion in Helmand province on Monday, taking the total number of British deaths in Afghanistan to 236, the defense ministry said.
Obama spoke to Brown, as well as French President Nicolas Sarkozy and Italian Prime Minister Silvio Berlusconi, on Monday on the new strategy, the White House said.
In October Brown said he would be prepared to send the extra troops -- taking Britain's force level to 9,500 -- as long as other coalition countries sent more soldiers, the right equipment was available and Afghan troops were trained faster.
Britain also has about 500 special forces soldiers in Afghanistan in addition to the main troops, Brown said.
There are about 110,000 foreign troops in Afghanistan, anchored by a 68,000-strong American force. While army chiefs have called for more soldiers, waning public support in Europe and the United States has made meeting such demands difficult.
Sarkozy said on Monday that France would keep its 3,400 troops in Afghanistan for as long as necessary but did not mention the possibility of sending more. We are not going to stay in Afghanistan indefinitely, he said.
Britain will host an international meeting on January 28 in London to discuss how best to transfer security to Afghan control.
Afghan President Hamid Karzai has said Afghans could be in charge of security within five years but that is likely to be contingent on tackling corruption and the success of Pakistan's offensive against militants on its border with Afghanistan.
Western leaders want a large increase in Afghan troops by the end of next year to 134,000, but military commanders say many more will be needed to allow NATO forces to withdraw.
Brown said the future stability of Afghanistan also required the non-interference of its neighbors.
(Additional reporting by Sophie Hardach in Paris; editing by Robin Pomeroy)