Prime Minister David Cameron has said he wants UK troops out of Afghanistan within five years.
Speaking in Canada, Mr Cameron said he wanted to see troops home by the time of the next general election, due in 2015, "make no mistake about it".
However, ahead of talks with US President Barack Obama on Saturday, Mr Cameron told Sky News he preferred not to "deal in too strict timetables".
Some 307 UK forces personnel have died since the Afghan mission began in 2001.
During the election campaign, Mr Cameron said he would like to see troops brought back during course of this Parliament.
Interviewed in Canada, where he will take part in the G8 and G20 summits, Mr Cameron told Sky News: "We can't be there for another five years, having been there for nine years already.
"But one thing we should be clear about - Britain should have a long-term relationship with Afghanistan, including helping to train their troops and their civil society, long after the vast bulk of troops have gone home."
His aides said his comments did not suggest any new timetable for bringing troops home.
BBC political editor Nick Robinson said while there was insistence the remarks did not indicate a new policy, the prime minister's declaration "does highlight the fact that his mind is on how and when to bring British forces out of Afghanistan".
Mr Cameron spoke as four UK soldiers who died in an accident in Afghanistan on Wednesday - the latest British fatalities there - were named by the Ministry of Defence.
Pte Alex Isaac, Pte Douglas Halliday, Colour Sgt Martyn Horton and L/Cpl David Ramsden were travelling in a Ridgeback armoured vehicle when it left the road and landed in a canal.
Mr Obama wants a US drawdown of troops to begin next summer although US General David Petraeus - who this week replaced the sacked commander of multinational forces Stanley McChrystal - is among those insisting that has to be based on conditions on the ground.
Asked about Mr Obama's preference, Mr Cameron said he would rather not "deal in too strict timetables" but wanted to get on with bringing "some stability" in Afghanistan so its people could run their own country and troops could come home.
In an interview with Canadian broadcaster CBC, Mr Cameron added that he wanted a "proper review" of progress towards the end of the year.
"I want this to be done, as far as possible, on the basis of success rather than lines in the sand and dates, but am I pushing very hard to get everything done so this can happen? Yes, of course."
He said there were three main aims - ensuring the troop surge works and counter-insurgency continues "full steam ahead", training the Afghan army and police, and achieving the political settlement needed "with those elements of the Taliban that want to lay down their weapons".
"Get those three things right and the timetables are realistic," he said.
Some 10,000 British soldiers are based in Afghanistan, many fighting a counter-insurgency campaign in the southern Helmand province.
Ministers say it is crucial to Britain's own security to ensure "a stable enough" Afghanistan to prevent it again becoming a haven for those who want to carry out attacks like 9/11.
British troops went to Afghanistan in November 2001 as part of an American-led invasion in the wake of the 9/11 attacks in the US.
The goal was to topple the Taliban who had given safe haven to al-Qaeda, although in the following years the aims of the British mission broadened.
Last summer the House of Commons Foreign Affairs Select Committee said British troops were trying to do too much and had experienced "mission creep".
It said the initial goal of supporting the US in countering international terrorism had stretched into the realms of "counter-insurgency, counter-narcotics, protection of human rights and state-building".
Following a visit to the country this month Mr Cameron warned further British casualties were likely over the summer, and said he wanted to bring troops home "the moment it is safe to do so".
He told MPs that while the threat from al-Qaeda in Afghanistan and Pakistan had reduced - he had been advised it would increase again if international forces left.