As Islamic militants methodically carved out a base in the desert of northern Mali over the past year, officials in Washington, Paris and African capitals struggling with military plans to drive the Islamists out of the country agreed on one principle: African troops, not European or American soldiers, would fight the battle of Mali.

But the surprise French assault last Friday to blunt the Islamists’ advance upended those plans and set off a cascading series of events, culminating in a raid on Wednesday by militants on a foreign-run gas field in Algeria. That attack threatens to widen the violence in an impoverished region and drag Western governments deeper into combating an incipient insurgency.

And yet the rush of events has masked the fact that officials in Washington still have only an impressionistic understanding of the militant groups that have established a safe haven in Mali, and they are deeply divided about whether some of these groups even pose a threat to the United States.

Moreover, the hostage situation in Algeria has only heightened concerns that a Western military intervention could transform militant groups that once had only a regional focus into avowed enemies of the United States — in other words, that the backlash might end up being worse than the original threat.