Most will go to Helmand province in the south in the run-up to the expected spring offensive by the Taliban.
Tony Blair, the British prime minister, said last week that 1,600 British personnel were being pulled out of southern Iraq.
"It's clear that, as overstretch hits hard, the government is having to scratch around to find anywhere from which it can withdraw troops to then send to Afghanistan," Liam Fox, the Conservative Party defence spokesman, said.
"Our armed forces are carrying a heavy and disproportionate burden in Helmand"
Liam Fox, Conservative Party defence spokesman
"Our armed forces are carrying a heavy and disproportionate burden in Helmand. As our deployment increases, more and more of our servicemen and women are feeling the pressure."
Nato countries including Germany, France, Italy and Spain have faced criticism for not contributing enough to the campaign, and last week Browne called for more nations to commit extra resources to the Afghan mission.
"Nato must respond to this request, or we will put at risk everything we have achieved across Afghanistan in the last five years: the stability which has brought five million refugees home and advances in democracy, the economy, human rights and women's rights, " Browne said.
Britain troops, which have had a presence in Bosnia for 15 years since the 1992-1995 conflict began, are involved in peacekeeping and reconstruction based near Banja Luka in the northwest.