KABUL, Afghanistan — France’s call for a speedier NATO exit from Afghanistan reflects the depth of war fatigue in the West and raises fears that other countries in the U.S.-led coalition will succumb to rising political pressure and pull their troops home early.

French President Nicolas Sarkozy’s decision to fast-track its withdrawal — just days after an Afghan soldier gunned down four French troops — is the latest crack in a coalition already strained by economic troubles in Europe and the United States, the Afghan government’s sluggish battle against corruption, on-again off-again cooperation from neighboring Pakistan and a dogged Taliban bloodied but not beaten.

The international coalition is already rushing against the clock to meet President Hamid Karzai’s goal of having the Afghan police and army in charge of the nation’s security by the end of 2014. France’s break with that timetable, which was agreed to by NATO members, now raises the question: Can the coalition stay together until then?

Resetting the date to end the coalition’s combat mission could strengthen arguments for President Barack Obama to accelerate U.S. troop withdrawals beyond the 33,000 he’s sending home by the end of this year, and reopen a debate over whether setting a withdrawal deadline allows the Taliban to seize more territory once foreign forces are gone.

It’s unclear whether Sarkozy’s call for all foreign forces to hand security over to the Afghan forces in 2013 will have any traction when it is presented next week at a NATO defense ministers’ meeting in Brussels. If other nations see France’s move as a green light to speed up their withdrawals, it will complicate the current strategy for a coordinated pullout.

In a gentle rebuke to France, British Prime Minister David Cameron said in London on Saturday that withdrawals should be dependent on security conditions on the ground. Britain has said it’s keeping to plans to withdraw its 9,500 troops from Afghanistan by the end of 2014.

“The rate at which we can reduce our troops will depend on the transition to Afghan control in the different parts of Afghanistan, and that should be the same for all of the members of NATO,” Cameron said after meeting with Karzai.

Other nations facing extreme economic problems, such as Italy and Spain, are not planning early withdrawals.

“We are a responsible country. We are a big country that honors its commitments that it agrees to make,” said Minister Giampaolo Di Paola, defense minister in Italy, which this week signed a pact aimed at supporting Afghanistan after foreign forces withdraw in 2014.

Germany also said it agrees with the goal to hand over security responsibility by the end of 2014 and withdraw combat troops.

Sarkozy said France will speed up its withdrawal and pull 1,000 — up from 600 — out this year and bring all combat forces home at the end of 2013. Sarkozy also said France would hand over authority in the province of Kapisa, where the French troops were killed this month, by the end of March.

France, which now has about 3,600 soldiers in the coalition force, joins the U.S., Britain, Germany and Italy in the top five largest troop-contributing nations.

Talk of an accelerated exit alarmed many Afghans, especially those who have cast their lot with the U.S.-backed government but have little confidence in their country’s own security forces. Some said France was reneging on its promises.

Afghan lawmaker Tahira Mujadedi, who represents Kapisa, said Afghan forces there aren’t ready to go it alone in fighting the Taliban insurgency, which is especially strong in several of the province’s districts. She warned that if NATO forces do pull back from Kapisa, it could also destabilize nearby Kabul. Foreign forces should consider staying even longer than 2014, she said.

“When military forces are present in a war zone, anything can happen,” said Mujadedi, who expressed sadness about the French troops who were killed.

But she added: “They are not here for a holiday.”

Former Afghan interior minister and military analyst Abdul Hadi Khalid said Sarkozy’s decision was clearly political. Sarkozy’s rival in spring presidential elections in France, Socialist candidate Francois Hollande, has pledged to pull French troops out of the war if he is elected in May.

“Why is he raising this now?” Khalid asked. “He is trying to get political benefit out of it.”

So far, Karzai has reacted cautiously to the idea of a 2013 handover. He can ill afford to anger major coalition partners, yet he wants to be seen as the leader of a country capable of security itself.

“We hope to finish the transition ... by the end of 2013 at the earliest — or by the latest as has been agreed upon — by the end of 2014,” Karzai said.

NATO spokeswoman Oana Lungescu underscored the coalition’s solidarity, saying that all nations agreed at a Lisbon summit in 2010 to complete the transition to Afghan-led security by the end of 2014.

“Transition is well on track to be completed by the end of 2014, as we all agreed,” she said. She said NATO nations would “take stock, shape the next stage of transition” at its summit in Chicago in May.

In Chicago, NATO members will discuss another contentious issue: Who will pay the salaries of the more than 300,000 Afghan policemen and soldiers after 2014. Estimates range from $5 billion to $6 billion a year.

Thomas Risse, a political scientist at Berlin’s Free University, said the problem of securing commitments to finance the Afghan security forces comes as a general fatigue with foreign interventions grips Europe and the United States.

“The public mood in most NATO countries is that they want their boys back as soon as possible and they don’t care much about Afghanistan either way,” Risse said. “The political elites have undertaken to keep up the military commitments, but I’m not sure they will be able to sustain those promises in the face of such a strong public mood.”

“As far as the money (for the post-2014 period) is concerned, I don’t think there is any mood in Germany to throw money after the Karzai regime,” he added.

Stories of Afghan security forces killing their foreign partners make it that much harder to sell the war in cash-strapped countries.

The deadly shooting of the four French soldiers on Jan. 20 was the second against French forces in a month; two members of the French Foreign Legion were killed by an Afghan soldier on Dec. 29. On Thursday, an Afghan man wielding a knife tried to attack foreign troops in southern Afghanistan before being arrested. The Taliban said the man was upset about a video that purportedly shows U.S. Marines urinating on Afghan corpses.

The promise to pull out by 2014 has appeased immediate public demand, said Malcolm Chalmers, a professor of defense at Kings College in London.

“But as the (economic crisis) continues to deepen and these types of incidents continue to occur, it’s very possible that there will be renewed public pressure to accelerate the pace of withdrawal,” he said. “My expectation is that there will be a steady and substantial withdrawal starting this year.”

Asked if France’s break with the coalition could spark a wider split, Kate Clark, senior analyst with the Afghanistan Analysts Network, said it could be troublesome for countries deploying troops to Afghanistan. While the U.S. contributes the bulk of troops, any cracks in the coalition could dampen morale of all foreign forces on the battlefield, she said.

“The foreign troops have been here for 10 years. That’s a long time,” she said. “There’s a certain war-weariness among the voters of a great many of those countries.”

Then again, she pointed out that the Netherlands and Canada have drawn down their forces in recent years and the coalition has not crumbled.