Terrorism has emerged once again as the central issue in the presidential campaign — but not in a way anyone expected. In the wake of attacks last week in New York, New Jersey and Minnesota, Hillary Clinton and Donald Trump have accused each other of being the candidate Islamic terrorists prefer.

Clinton started it — this week’s round, at least. She came out swinging on Monday, saying Trump’s rhetoric made him a “recruiting sergeant” for Islamic State. “The language that Mr. Trump has used is giving aid and comfort to our adversaries,” she said. (“Aid and comfort” is part of the Constitution’s definition of treason.)

Trump, who earlier accused President Obama and Clinton of being the “founders” of Islamic State, fired back. “Terrorists all over the world … are hoping and praying that Hillary Clinton becomes president,” he said. “They want her so badly to be your president, you have no idea,” he added later. “It will be a field day.”

It’s dangerous to call anything unprecedented, but I can’t remember a presidential campaign in which the candidates accused each other of being in league, wittingly or not, with the nation’s worst enemies.

During the Cold War, Republicans sometimes accused liberal Democrats of being soft on communism — but usually painted them as dupes, not co-conspirators.

When many Americans are gripped by fear of terrorist strikes in city streets or shopping malls, this is pretty rough stuff.

It should go without saying that neither Islamic State nor any other terrorist group has endorsed either candidate. (If they did, the result could be dramatic.)

But on the facts, Clinton has the better of this argument. This spring, spokesmen for Islamic State celebrated Trump’s proposals to ban Muslim immigration to the United States apparently because they believed it would sharpen the clash of civilizations the extremist group wants to provoke. “I ask Allah to deliver America to Trump,” one wrote.

That’s why former CIA director Michael Hayden, a George W. Bush appointee, has criticized the GOP nominee on this issue. “When Trump says they all hate us, he’s using their narrative,” Hayden told the Guardian newspaper. “He’s feeding their recruitment video.”

Contrary to what Trump said, there’s no record of any Islamic State spokesmen saying they want Clinton to win. The GOP nominee claimed that the terrorists prefer Clinton’s policies to his, but there’s no evidence of that either.

Trump’s argument is that Clinton, as secretary of State under President Barack Obama, shares responsibility for allowing Islamic State to rise. “We’ve been very gentle” to Islamic State, he claimed on Monday, seemingly ignoring the almost 12,000 airstrikes U.S. forces have carried out against the group since 2014.

“We’re going to have to do something extremely tough over there,” he told Fox News.

“Like what?” a Fox anchor asked.

“Like knock the hell out of them,” Trump said. That’s about as specific as he gets.

Trump has offered two more proposals: He wants to increase ethnic and religious “profiling” to identify possible terrorist sympathizers in the United States. (He claims profiling isn’t used now, but he’s wrong about that; federal policy explicitly allows it in terrorism cases.) And he wants to impose “extreme vetting” on foreigners entering the United States. (Clinton has called for “tough vetting.”)

Here’s the political surprise in this brawl: Clinton could come out ahead.

It’s not at all clear that terrorist attacks, and the fears they sharpen, automatically produce votes for Trump. That’s not what happened after the attack on an Orlando nightclub in June, where 49 died. After that incident, the polls moved only a little — and in some surveys, Clinton’s standing improved.

Indeed, Clinton’s quick offensive on this issue revealed how she wants to frame the voters’ choice: Which candidate do you want to put in charge of the armed forces?

In normal election years, most voters say they think the Republican candidate, with the GOP’s hawkish history, is better qualified to deal with terrorism.

But this isn’t a normal year. In a Fox News poll released last week, more voters said Clinton would do a better job dealing with terrorism than would Trump, by 47 percent to 46 percent. Although those numbers are within the poll’s margin of error, they still mean the GOP has lost its usual advantage. Other surveys have shown similar results.

Clinton’s argument is that Trump — with his ill-considered, self-indulgent, hair-trigger responses — is too erratic to be president. She’s doing her best to keep the words “commander in chief” in the air.

In a focus-group discussion with undecided voters last week, several said that issue was weighing heavily on their minds.

“I really dislike Hillary,” said Cameron Scott, a retired bus driver from Alexandria, Va. “But he’s just plain scary. I can’t vote for him.”

Doyle McManus is a columnist for the Los Angeles Times. Readers may email him at doyle.mcmanus@latimes.com.