U.S. military commanders are stepping up their fight against Islamist extremism as President Donald Trump’s administration urges them to make more battlefield decisions on their own.

As the White House works on a broad strategy, America’s top military commanders are implementing the vision articulated by Defense Secretary Jim Mattis: Decimate Islamic State’s Middle East strongholds and ensure that the militants don’t establish new beachheads in places such as Afghanistan.

“There’s nothing formal, but it is beginning to take shape,” a senior U.S. defense official said Friday. “There is a sense among these commanders that they are able to do a bit more—and so they are.”

While military commanders complained about White House micromanagement under former President Barack Obama, they are now being told they have more freedom to make decisions without consulting Mr. Trump. Military commanders around the world are being encouraged to stretch the limits of their existing authorities when needed, but to think seriously about the consequences of their decisions.

The more muscular military approach is expanding as the Trump administration debates a comprehensive new strategy to defeat Islamic State. Mr. Mattis has sketched out such a global plan, but the administration has yet to agree on it. While the political debate continues, the military is being encouraged to take more aggressive steps against Islamic extremists around the world.

The firmer military stance has fueled growing concerns among State Department officials working on Middle East policy that the Trump administration is giving short shrift to the diplomatic tools the Obama administration favored. Removing the carrot from the traditional carrot-and-stick approach, some State Department officials warn, could hamper the pursuit of long-term strategies needed to prevent volatile conflicts from reigniting once the shooting stops.

The new approach was on display this week in Afghanistan, where Gen. John Nicholson, head of the U.S.-led coalition there, decided to use one of the military’s biggest nonnuclear bombs—a Massive Ordnance Air Blast bomb, or MOAB—to hit a remote Islamic State underground network of tunnels and caves.

A senior administration official said Mr. Trump didn’t know about the weapon’s use until it had been dropped.

Mr. Mattis “is telling them, ‘It’s not the same as it was, you don’t have to ask us before you drop a MOAB,’” the senior defense official said. “Technically there’s no piece of paper that says you have to ask the president to drop a MOAB. But last year this time, the way [things were] meant, ‘I’m going to drop a MOAB, better let the White House know.’”

The more aggressive military approach comes as the long slog against Islamic State is bearing fruit. The group is on the back foot in its Iraqi stronghold, Mosul, and is facing a hard battle to defend its de facto Syrian capital, Raqqa.

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