NAIROBI, Kenya — For nearly a decade, the United States has been trying to fight the Somali Islamist group known as the Shabab, using everything from its African allies and economic sanctions to American missile strikes and commando raids.

On Tuesday, Pentagon officials announced that they had conducted American airstrikes to go after the leader of the Shabab directly, striking at the heart of a militant group that has allied itself with Al Qaeda and terrorized the region for years.

Rear Adm. John Kirby, the Pentagon press secretary, said military officials were trying to assess whether the Shabab leader, Ahmed Abdi Godane, had been killed in the strikes, which took place on Monday on an encampment and a vehicle south of Mogadishu, the capital. The attack was carried out by Special Operations forces using both manned and unmanned aircraft, launched, Admiral Kirby said, based on “actionable” intelligence that Mr. Godane was at the encampment.

The American warplanes dropped a number of Hellfire missiles and precision bombs. Defense officials said they believed that both the encampment and the vehicle had been destroyed, and that the militants there had been killed. But they were still trying to determine the fate of Mr. Godane.