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State Department spokeswoman Victoria Nuland said that U.S. law prohibited any direct aid to the Malian military, because of the coup its commanders engineered last year, which overthrew the president and provoked the northern Islamists to rebel.

But the United States could aid the French, who would be fighting alongside the Malian military and the African-led peacekeeping force, whenever it eventually deploys.

“We are precluded under the countercoup restrictions from funding a military that has been involved in a coup until democracy has been restored,” Ms. Nuland said, “But we’re not precluded from assisting allies and partners in trying to restore security to that country.”

Mr. Hollande last week also persuaded Mr. Obama to support a French military operation in Somalia, where special forces were trying to rescue a French hostage from militants. U.S. fighter planes entered Somali airspace in the operation on Friday, but didn’t use their weapons, the White House said. The rescue mission failed with the apparent death of the hostage and the killing of at least one French commando.

Asked if the U.S. is expanding its front in the fight against terrorism in North Africa, Mr. Carney replied, “We obviously work with our allies in an effort to deal with al Qaeda and its affiliates around the world and around both the Middle East and North Africa and elsewhere.”

Mr. Hollande, visiting the Persian Gulf region to drum up support for the French intervention, vowed Tuesday that French forces will not leave until the country is stable — raising the prospect of a lengthy operation.

“We have one goal: to ensure that when we leave, when we end our intervention, Mali is safe, has legitimate authorities, an electoral process, and there are no more terrorists threatening its territory,” Mr. Hollande told a news conference Tuesday in the United Arab Emirates, according to Reuters.

Vocal support for the French also came from the chairman of the House Foreign Affairs Committee, who called Tuesday for the Obama administration to “honor appropriate requests for intelligence and logistics support from France.”

“When confronting a shared threat, we should have our ally’s back,” said Rep. Edward R. Royce, California Republican.

“I welcome France taking the initiative to combat this serious security threat in North Africa,” said Mr. Royce, adding that their control of northern Mali gave “these al-Qaeda-linked militants space to operate, and the weapons flowing out of Libya makes them deadly.”

“This cancer could not go unaddressed,” the committee chairman said.

A spokesman for the Taliban in Afghanistan, Zabihullah Mujahid, said France “has launched war against the Muslim nation of Mali without having any legal jurisdiction.”

“Such interventions and attacks are not only disastrous for Mali, but also for France,” he said. “All the powerful countries of the world should take lessons from the failed American policy of military interventions in Afghanistan and Iraq, from which it cannot wrangle free or regain its lost status.”