BECKLEY, W.Va. — When Mitt Romney stumped here Tuesday for a trio of Republican candidates for Congress, the event had all the trappings of a “Romney for President” rally.

The crowd chanted, “Mitt! Mitt! Mitt!” They applauded loudest when the 2012 Republican standard-bearer took center stage, eclipsing the three Republican candidates who actually will be on West Virginia ballots in November.

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Outside the event, union activists demonstrated. They denounced Mr. Romney as a “fat cat” and the “king of exporting jobs.”

Mr. Romney endured the same kinds of attacks during his run as the 2012 Republican presidential nominee.

Just about everyone attending the rally — the Republican candidates, party donors, reporters — pestered Mr. Romney privately and publicly about whether he will run for president again.

Each time, Mr. Romney insisted that he would not run. He has made that claim repeatedly as supporters clamor for his candidacy and his actions — if not his words — send mixed signals about his intentions.

“I’m not running,” Mr. Romney told reporters after the rally. “I’m expecting to be getting behind some good people or a good person who will be [the Republican nominee].”

The former Massachusetts governor has some pointed words for the man who defeated him two years ago, saying President Obama was doing “a good deal worse than even I expected.” He cited the U.S. economy and troubles abroad in such hot spots as Iraq, Syria and Russia.

“I was not a big fan of the president’s policies, as you know, either domestically or internationally,” he said, “but the results of his mistakes and errors, in my opinion, have been more severe than even I would have predicted.”

Despite his demurrals about a political future, Mr. Romney’s itinerary may suggest otherwise.

He has put himself at the forefront of Republican midterm campaigns by endorsing more than three dozen candidates, headlining a series of party fundraisers and stumping in key races.

He hits the campaign trail for Republican candidates in states he won in 2012 and where he remains popular, such as West Virginia. He was the first Republican presidential candidate to win all of the state’s 55 counties.

But Mr. Romney also has also campaigned in crucial presidential primary states such as Iowa and New Hampshire.

This week, Mr. Romney is barnstorming across the country to lend a hand in Senate and House races.

He started with a rally in Florida with Carlos Curbelo, who is running in the Republican primary to challenge Democratic Rep. Joe Garcia.

In this south-central West Virginia town, he appeared with Republican Shelley Moore Capito, who leads in the polls against Democrat Natalie Tennant in the contest for an open U.S. Senate seat; Republican Evan Jenkins, who is in a tight race to unseat incumbent Democrat Rep. Nick J. Rahall II; and Republican Alex X. Mooney, who is running against Democrat Nick Casey for an open House seat.

He headed next to North Carolina to boost Republican Thom Tillis, the state House speaker who is running to unseat Democratic Sen. Kay R. Hagan, and then to Arkansas to support Republican Asa Hutchinson’s run for governor.

Next month, Mr. Romney is scheduled to appear at a fundraising event in Virginia for Republican Barbara J. Comstock, who is facing Democrat John W. Foust in the race to replace retiring GOP Rep. Frank R. Wolf.

Still, campaigning with Mr. Romney can be double-edged.

Democrats criticized Mrs. Capito for teaming up with Mr. Romney, whom they accused of being anti-coal because as governor he said a Massachusetts coal-fired power plant needed to be cleaned up because it “killed people.”

“Actually, I’m not running for anything. So, I don’t have to worry too much about it,” Mr. Romney said when a local TV reporter asked about his comment from 2003.

Mr. Romney was pressed about how the comment reflected on Mrs. Capito in West Virginia coal country.

“Fortunately, she has her own positions and she doesn’t have to accept all of mine,” he said. “But the other thing is, I did run for president twice and I think I made it very clear in my presidential campaigns that I’m a friend of coal.”

Mrs. Capito stood by Mr. Romney.

“Gov. Romney endorsed us today, and it means a lot to me,” she said. “As every West Virginian knows, all 55 counties in West Virginia voted to have Gov. Romney be our president, and we are regretful that it didn’t work out.”

The flurry of campaign activity by Mr. Romney has fueled speculation that he has not abandoned his White House hopes.

The fledgling movement to draft Mr. Romney for 2016 has been buoyed by polls showing he would beat Mr. Obama in a rematch.

A CNN poll last month showed Mr. Romney winning the popular vote by 53 percent to 44 percent, a larger margin of victory than the 2012 results in which Mr. Obama won the popular vote 51 percent to 47 percent.

Mr. Romney joked about the idea of an election rematch.

“Wouldn’t that be nice?” he said with a laugh. “But that’s not the reality of how the world works. Of course, the president won fair and square, and I respect the fact that he’s the president and hopefully he’s able to do what it takes to get America going again.

“I’m delighted that some people recognize that I would have been a good president,” he said. “That’s a nice thing to hear, but I’m not worried about the past, I’m much more worried about what our future looks like, and if we elect people like Shelley Moore Capito to take that leadership role, you’ll see a brighter future.”

Mr. Romney couldn’t resist stoking the West Virginia crowd with talk of 2016.

“I don’t know what’s going to happen in 2016. I sure want to see a Republican president,” he said, provoking a thunderous eruption of cheers and applause. “I’m going to be supporting one of the good guys who’s going to be running in 2016.”

Mr. Romney steered his speech back to the candidacy of Mrs. Capito, whose victory is crucial to Republican efforts this year for a net pickup of six seats to win majority control of the Senate.

“Right now, we need to elect people to go to Washington who can pass bills to make some changes and send them to President Obama’s desk, and then if he vetoes it he’ll be the guy that’s the party of no,” Mr. Romney said. “We’ll make sure people understand that we’ve got ideas to get this country working again [and] we’re going to do it. We’re going to get wages up and jobs up.”

He said he was proud that Mrs. Capito would be in the Senate to “shake things up.”

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