But France made clear its position on the issue on 3 October, when the Afghan president met in Paris with French Prime Minister Dominique de Villepin and Defense Minister Michele Alliot-Marie.
French Defense Ministry officials say Alliot-Marie told Karzai that Paris wants the U.S.-led counterterrorism combat mission and the UN-mandated stabilization efforts in Afghanistan to remain separate.
NATO spokesman James Appathurai says the issue was part of a broad debate between NATO defense ministers when they gathered last month in Berlin for an informal meeting.
"The secretary-general [of NATO, Jaap de Hoop Scheffer] wanted [NATO] defense ministers to lift their eyes and look to the future -- to see what kind of strategic environment they foresaw 10 to 15 years from now and how they thought NATO should plan and shape its armed forces and its missions to meet the challenges of that security environment," Appathurai said. "So there was a very open and very political discussion amongst defense ministers about where they saw the future of the alliance -- and the balance, for example, that they foresaw between the requirement for stabilization forces or high-end combat forces."
Appathurai says the NATO ministers agreed that there would be closer links between the International Security Assistance Force (ISAF) and the antiterrorism coalition currently led by the United States.
"Defense ministers did two things. One, they stressed NATO's long-term role and looked forward to the expansion of the International Security Assistance Force to the south of the country from where it is now, in the capital, and in the north and the west," Appathurai said. "And then [they were] looking farther forward to where NATO will take responsibilities throughout the country. But this, of course, requires ever closer synergy between the NATO mission and Operation Enduring Freedom -- that is the coalition-led mission that is now predominantly in the south and the east of the country, and that focuses more on counterinsurgency and counterterror operations."
Appathurai says debates will continue within NATO for months about a formal command structure for antiterrorism combat missions in Afghanistan. But he says whatever the outcome, there will be greater synergy and cooperation between ISAF and coalition forces -- with both moving closer together, both geographically and in terms of mutual support.
Ian Kemp, an independent defense analyst based in London, says he is not surprised by the emerging debate.
"The French statement is consistent with the policy that France and some of the other NATO countries, including Germany, have had consistently over the past few years," Kemp says. "Certainly since the U.S.-led coalition has become involved in Afghanistan, France, Germany, and some of the other NATO allies do not want to see the alliance take over responsibility for the combat mission. There has always been reluctance to do this."
Kemp says Washington's position is based on the need to reduce its military presence in Afghanistan following September's parliamentary elections.
"There's no doubt of it. The Americans would like to transfer command for the operation in Afghanistan to NATO so they can concentrate their attentions fully on what is happening in Iraq. The United States is aware that many of the NATO allies are not going to be prepared to contribute troops to Iraq. We've already seen that [for] some of the NATO allies, domestic pressure has forced them to withdraw troops. The mission in Iraq is very unpopular. So I think the United States realizes they're not going to get more of the NATO nations into Iraq. So they'd like to see NATO take over a much bigger role in Afghanistan," Kemp says.
There is no direct evidence that Karzai has been pressured by Washington to call for NATO to take over the command of coalition forces in Afghanistan. But Dominique Moisi, the deputy director of the Paris-based French Institute for International Relations, says such criticisms are understandable.
"Without the United States, the regime of Karzai would not be in place. He knows what he owes to Washington. And globally speaking, in comparison with the situation in Iraq, the situation in Afghanistan is a relative success. But clearly a success," Moisi says.
Moisi tells RFE/RL that Operation Enduring Freedom's command structure is not as significant as a guarantee that countries will continue to send troops to Afghanistan.
"I think by the end of the day, who is in charge is less important than the issue [of] 'Are you there? Are you willing to help?' So I don't think we should overemphasize formalism when it comes to the organization of the forces," Moisi says.
Kemp tells RFE/RL that even if NATO does take over the command of combat operations in Afghanistan, the alliance will continue to rely on U.S. military assets.
"The sort of capabilities that the United States is providing now would be airlifts, strategic intelligence -- the full spectrum, from satellite surveillance to unmanned air vehicles. And also, the combat operation now is very heavily supported by U.S. helicopters -- both the big Chinook troop lift carrying helicopters and also the Apache attack helicopters. That's the sort of capability that would be difficult for NATO to duplicate," Kemp says.
Kemp concludes that French and German opposition to NATO command over Operation Enduring Freedom is likely to prevail. But he says that won't stop the alliance from taking on a bigger role in Afghanistan as U.S. troops are shifted elsewhere.
"I don't think we're going to see any significant shift in the French position toward actually accepting NATO command of the combat operation. But the alliance is extremely flexible and can always come up with a compromise. What I think we're going to see next year when the United Kingdom assumes command of the [ISAF] mission, is that there's going to be an expanded British presence," Kemp says. "There's going to be an expanded Canadian presence. NATO has asked the Australians to contribute more troops. It's quite possible we might see what some people term as 'mission creep' -- once Britain is in command of the [ISAF] mission, the extent of the mission slowly expanding."
Representatives of NATO's top decision-making body are to visit Kabul later this week to discuss plans to expand ISAF's mission into southern Afghanistan -- where the U.S.-led coalition continues to fight remnants of the Taliban and Al-Qaeda.
ISAF spokesman Andrew Elmes says the delegation from the North Atlantic Council will meet with Afghan and international officials involved in security.