British Prime Minister Gordon Brown urged Afghanistan and Pakistan yesterday to cooperate more closely against terrorism at a time of increased political uncertainty and an upsurge in violence.

Mr Brown also said Britain should brace itself for more military deaths in Afghanistan in the wake of a Taliban ambush that killed 10 French paratroopers.

Pakistan's political leaders are trying to agree a way forward after President Pervez Musharraf - a key ally of the West on counter-terrorism - resigned this week.

Mr Brown, briefing reporters en route to the Olympics in Beijing, said it was essential Afghanistan and Pakistan stepped up security on their border, which has become a safe haven for Taliban insurgents.

"This cooperation between Afghanistan and Pakistan is absolutely essential for the future," Mr Brown said.

Asked if Mr Musharraf's departure could hinder the fight against terrorism, Mr Brown said Britain worked very closely with Pakistan's "strong army" and army chief General Ashfaq Kayani.

He also stressed the need for Afghan President Hamid Karzai to root out corruption in his administration and to ensure economic aid was delivering results on the ground. Mr Brown said Britain's strategy in Afghanistan - where it has some 8,400 troops - was working in terms of building up the Afghan army, but he said the Taliban's summer offensive was always expected to be fierce.

"We know we've got to be prepared - we're fighting a very difficult campaign - for anything that may happen," he added.

Mr Brown said he did not feel Britain needed to send additional troops to Afghanistan but repeated his call for other Nato members to do more.

"I've been pressing... for an increase in the burden sharing by other countries."

Asked about the crisis between Russia and Georgia, Mr Brown urged Moscow to withdraw fully from the country and said he and others in the West had expressed "outrage" at its actions.