David Cameron has welcomed Barack Obama's announcement that the US will withdraw about one-third of its forces from Afghanistan next year.
After the US president declared the fight against al-Qaida and the Taliban a success, Cameron, in a statement issued on Thursday, said the UK would keep its own force levels in Afghanistan "under constant review".
"I have already said there will be no UK troops in combat roles in Afghanistan by 2015 and, where conditions on the ground allow, it is right that we bring troops home sooner," the prime minister said.
Obama's statement was also welcomed by General Sir David Richards, the chief of the defence staff, but received a more cautious reaction from the former army chief General Sir Richard Dannatt, who described the move as "bold but risky".
Obama said 33,000 US troops would be withdrawn by the summer of 2012, or by September that year at the latest. The first 5,000 would return next month, with another 5,000 following by the end of the year.
The president said that when he ordered the 33,000 extra troops to Afghanistan in 2009 they had a clear mission – to refocus on al-Qaida, reverse the Taliban's momentum and train Afghan security forces to defend their country.
"Tonight, I can tell you that we are fulfilling that commitment," he said. "We are meeting our goals."
Obama claimed al-Qaida was under more pressure than at any time since the 9/11 attacks on New York and Washington. Half its leadership has been killed, including its leader, Osama bin Laden. "This was a victory for all who have served since 9/11," the president said.
He addressed criticism that the US should not be spending billions on wars overseas while the country is struggling economically and promised to shift from foreign to domestic issues. "America, it is time to focus on nation building here at home," he said.
But US and other Nato military chiefs fear the president is taking a gamble with the scale of early drawdown, ignoring the advice of US and Nato commanders who have warned that withdrawal of anything more than a few thousand troops in the coming months could endanger substantial gains made in the battle against the Taliban over the winter.
US and Nato commanders argued that they could handle the withdrawal of about 5,000, mainly support staff, but warned that 10,000 this year would create logistical problems and interfere with the summer "fighting season".
The French president, Nicolas Sarkozy, announced on Thursday that he would order a gradual withdrawal of some of France's 4,000 troops in the country "in a calendar comparable to the withdrawal of American reinforcements".
The French defence minister, Gerard Longuet, said the details of the withdrawal would be kept quiet to avoid giving information to the Taliban.
Cameron was among the leaders the US president informed of his decision by phone.
The prime minister said the right conditions were in place to transfer security to the Afghans from next month.
"The surge by the US and international partners, supported by an increase in the number of Afghan army and police, has reversed the momentum of the insurgency and created the right conditions for security responsibility to begin to transfer to the Afghans from July," he said.
"We remain side by side with Afghanistan and our international partners to achieve a military and political solution in Afghanistan that will allow the Afghan people to take full responsibility for their own sovereignty and national security."
Dannatt said Obama deserved credit for backing a surge of troops, which he said had had a "beneficial effect" and left many areas more secure than they were. If troops were reduced by both the US and the UK, it was important to ensure the overall effort was maintained, he added.
"I think you have got to give him credit," Dannatt said. "He took the arguments here 18 months ago and agreed to the surge ... and they have had a real effect, undoubtedly.
"He wants to reduce the troops now, probably largely for domestic reasons and that is how it is ... other parts of the mission have got to step up to the plate and build a more stable life for the Afghan people."
William Hague, the foreign secretary, said the pace of withdrawal of UK troops would depend on the security situation in Afghanistan.
"Between now and 2015, the level of British forces, the pace of any reductions, depends on the progress we make, the conditions on the ground, the consultations with our allies," he said.
The foreign secretary explained that Afghan forces would be expected to take over security operations by 2014, allowing British forces to leave the year after.
Speaking from Kabul, Hague insisted all UK military chiefs were aware of the "unequivocal" deadline.
"We have said that, by 2015, British forces will not be engaged in combat in Afghanistan or in anything like the numbers that they are now. What happens between now and 2015 depends on conditions on the ground and our continuing assessment of those," he told BBC Radio 4's Today programme.
"One of the conditions is that by 2015 we reach that point ... I can tell you there are no ifs, no buts about that."
Hague also confirmed that talks were under way with Taliban elements and said Britain was "active" in that process.
"Contacts do take place with the Taliban," he said. "President [Hamid] Karzai has spoken about this in the last week, and so has [US defence] secretary [Robert] Gates."
But Jim Murphy, the shadow defence secretary, warned that a withdrawal of troops could leave a political "vacuum" in Afghanistan.
"There's a huge amount of work that is going into two areas," he told Sky News. "One, politics. As the military effort diminishes, the danger of a vacuum is created and the Taliban fills that and al-Qaida starts to return to Afghanistan. We have to have stability in the Afghan government.
"Secondly, to support that, we need Afghan forces that are strong enough. We've got a long way to go. The UK is doing a lot, but there is a long way to go on the Afghan army and an enormous way to go on the police."
In a statement, Richards said: "The prime minister has said we will not have combat forces in Afghanistan by the end of 2014. It is right at this time to recognise the tremendous efforts the American military has made and continues to make in Afghanistan, both in the performance of its forces and the leadership it provides."
He said the insurgency across Afghanistan was under "real and sustained pressure".