WASHINGTON — When Adm. Harry B. Harris Jr., the military’s top commander in the Pacific, ordered the aircraft carrier Carl Vinson “to sail north” from Singapore this month, he was oblivious to the larger — and incorrect — impression that he was rushing a naval strike force to confront an increasingly belligerent North Korea.

Four days later, when Gen. John W. Nicholson Jr. dropped the most powerful conventional weapon in the American arsenal on Islamic State fighters in a tunnel complex in eastern Afghanistan, he not only seized headlines around the world but also unintentionally signaled to dictators in Syria and North Korea that they might be the next target of what the Pentagon called the “mother of all bombs.”

Instead of simply achieving tactical objectives, the timing of their actions surprised their bosses at the Pentagon, upset edgy allies and caught the White House flat-footed. Taken together, the episodes illustrate how even the military’s most seasoned four-star field commanders can fail to consider the broader political or strategic ramifications of their operational decisions, and some current and former senior officials suggested that President Trump’s decision to unshackle the military from Obama-era constraints to intensify the fight against terrorists risked even more miscues.

“There are lots of decisions that military commanders make every day on their own without asking, ‘Mother, may I?’” said Robert M. Scher, a former senior Pentagon official. “But they have to realize and take into account that their actions can have strategic impact outside of their areas of responsibility.”

American officials said Thursday that General Nicholson had not requested permission from Mr. Trump, Defense Secretary Jim Mattis or Gen. Joseph F. Dunford Jr., chairman of the Joint Chiefs of Staff, before dropping the giant bomb, a GBU-43/B Massive Ordnance Air Blast, or MOAB.

And it does not appear the White House was aware of the location of the carrier group when the press secretary, Sean Spicer, or the national security adviser, Lt. Gen. H.R. McMaster, made their public comments about it. White House officials said both men were relying on talking points supplied by the Pentagon.

General Nicholson already had the necessary authority to bomb the tunnel complex and had it during the Obama administration as well, American officials said.

But current and former Defense Department officials said that if President Barack Obama were still in office, General Nicholson would probably have checked with his bosses before calling in the country’s most powerful non-nuclear bomb, because the Obama White House had made clear to the Pentagon that the president wanted to be consulted on major strike decisions.

“Nicholson should have been a little more aware that using that weapon for the first time would be a big story,” Mr. Scher said.

Mr. Trump has made clear that he does not want to be consulted on every strike, and that he wants commanders in the field to have more authority to move swiftly against foes.

The timing of the episodes, at the beginning of the Trump administration, most likely played a part, one Obama administration official noted.

“Once the previous administration’s political appointees have departed, the balance of power in the Pentagon always…