MARA, Chad — From Yemen to Syria to here in Central Africa, the Trump administration is relying on Special Operations forces to intensify its promised fight against the Islamic State and other terrorist groups as senior officials embrace an Obama-era strategy to minimize the American military’s footprint overseas.

In Africa, President Trump is expected to soon approve a Pentagon proposal to remove constraints on Special Operations airstrikes and raids in parts of Somalia to target suspected militants with the Shabab, an extremist group linked to Al Qaeda. Critics say that the change — in one of the few rejections of President Barack Obama’s guidelines for the elite forces — would bypass rules that seek to prevent civilian deaths from drone attacks and commando operations.

But in their two months in office, Trump officials have shown few other signs that they want to back away from Mr. Obama’s strategy to train, equip and otherwise support indigenous armies and security forces to fight their own wars instead of having to deploy large American forces to far-flung hot spots.

“Africans are at war; we’re not,” said Col. Kelly Smith, 47, a Green Beret commander who fought in Iraq and Afghanistan and was a director of a counterterrorism exercise in Chad this month involving about 2,000 African and Western troops and trainers. “But we have a strategic interest in the success of partners.”