The final document mentions “radical Islamist terrorism,” a term that refers to acts of terrorism by Sunni Muslim-affiliated networks like the Islamic State, according to a senior administration official, who spoke on the condition of anonymity to discuss the report before its release.

But by substituting “Islamist” for “Islamic,” the official said, the strategy seeks to avoid condemning Islam as a whole.

The new strategy bears the imprint of Mr. Bolton with its emphasis on the threat from Iran, which he described in a White House briefing as “the world’s central banker of international terrorism since 1979,” supporting militant and terrorist groups across the Middle East. Iran’s role was previewed in the State Department’s annual list of global terrorist threats last month.

The strategy set an uncompromising goal, declaring, “We will eliminate terrorists’ ability to threaten America, our interests and our engagement in the world.” And it embraced the martial language that former President George W. Bush used after the Sept. 11, 2001, attacks. “We are a nation at war,” the document said, “and it is a war that the United States will win.”

That reverses a position taken by former President Barack Obama, who said in May 2013: “Our systematic effort to dismantle terrorist organizations must continue. But this war, like all wars, must end.”

Mr. Bolton argued that it was wrong to lull Americans into thinking that the war on terror, which he characterized as a long ideological struggle, was over. “The idea that somehow we can just say, ‘Well, we’re tired of this war and it will go away,’ I think is a mistake,” he said.

In contrast to Mr. Trump’s confident public statements, the report took a sober view of the threat posed by the Islamic State. Despite losing all but 1 percent of the territory it previously seized in Iraq and Syria, it remains a potent threat to the United States, the document said.