Asked if fighters from Al Qaeda in the Islamic Maghreb posed such an imminent threat, Gen. Carter F. Ham, the top American commander in Africa, said, “Probably not.” But, he said in an interview, “they subscribe to Al Qaeda’s ideology” and have said that their intent is to attack Westerners in Europe and, “if they could, back to the United States.”

Defense Secretary Leon E. Panetta made it clear on Wednesday that he considered the group a serious danger. “This is an Al Qaeda operation,” he told reporters while traveling in Italy, “and it is for that reason that we have always been concerned about their presence in Mali, because they would use it as a base of operations to do exactly what happened in Algeria.”

It is too early to judge the impact of the French-led offensive in Mali, which came after an urgent plea by Mali’s government for help in repelling Islamist fighters who were rapidly moving south. But on Wednesday, some American officials said that the hostage episode in Algeria could be just the beginning of a wave of attacks against foreigners in the region. And there is a chance that if the Americans taken hostage on Wednesday are killed by their captors, American officials might reconsider their pledges not to commit ground troops to the battle.

As Islamists have tightened their grip on northern Mali over the past year, the American military has expanded spying operations in the region in the hope of gathering intelligence both about the strength of the militants and about their connections to tribal groups in Mali and elsewhere across North Africa.

According to current and former American government officials, as well as classified government cables made public by the group WikiLeaks, in recent years the military has set up a constellation of small bases in Africa for aerial surveillance missions flown by turboprop planes designed to look like civilian aircraft. One of the principal bases used for the missions in Mali is in Ouagadougou, the capital of Burkina Faso, according to one former official and the government cables.

But the surveillance missions in northern Mali have had only a limited effect. Islamist leaders have cracked down on some electronic communications and been careful not to reveal pieces of sensitive information that could be monitored, like their exact positions.