WASHINGTON — President Trump has let the military know that the buck stops with them, not him. The Pentagon, after eight years of chafing at what many generals viewed as micromanaging from the Obama White House, is so far embracing its new freedom.

Officials say that much of Defense Secretary Jim Mattis’s plan to defeat the Islamic State, which Mr. Mattis delivered to the White House in February but has yet to make public, consists of proposals for speeding up decision-making to allow the military to move more quickly on raids, airstrikes, bombing missions and arming allies in Iraq, Syria and elsewhere. Commanders argue that loosening restrictions — as Mr. Trump has already done for American operations in much of Somalia and parts of Yemen — could lead to a faster defeat of Islamic State militants in not only the Middle East but also the Horn of Africa.