FREDERICKSBURG, Va. — Donald Trump hasn’t given up the fight to win back Virginia for the Republican Party in November, but he is battling strong political headwinds that have the once solidly red state poised to vote Democrat for the third consecutive presidential election.

Democratic presidential nominee Hillary Clinton holds one of her biggest advantages among battleground states in Virginia, where she leads Mr. Trump by as much as 12 percentage points in polls. She has made the Old Dominion an anchor for her electoral strategy, which she underscored by tapping the state’s former governor, Sen. Tim Kaine, as her running mate.

Mr. Trump pushed back Saturday at a rally in this bedroom community on the southern edge of Northern Virginia, where his supporters reeled at the thought of their state remaining blue this year.

“It makes me absolutely sick that most Virginia goes red and a few cities will decide which way it goes,” said Billy Scogin, 36, a maintenance worker.

Like many other Trump supporters in Virginia, Mr. Scogin hoped President Obama’s two wins in the state were aberrations caused by racial politics, including overwhelming support from minorities and Mr. Obama’s broad appeal in making history as the country’s first black president.

Sean Perry, a banker from nearby Fauquier County, agreed.

“The biggest thing Trump needs to do is reach out to the black community. He’s got to get his feet in the cities and the suburbs,” he said. “It’s the only thing Hillary has.”

Indeed, the Clinton strategy hinges on the same elements that made Mr. Obama the first Democratic presidential candidate to win Virginia since 1964: support from the vast influx of Democratic voters in the rapidly growing Northern Virginia suburbs of Washington and heavy turnout from black voters, particularly in the Richmond and Hampton Roads areas.

Signaling the Clinton campaign’s growing confidence, the largest pro-Clinton super PAC announced last week that it would suspend its TV ad campaign in Virginia. Priorities USA Action, a group that was formed to support Mr. Obama and now backs Mrs. Clinton, also pulled ads in the crucial battlegrounds of Pennsylvania and Colorado.

What’s more stunning is that the Trump campaign left Virginia out of its first TV ad blitz that began Friday. The $1.4 million reserve of TV time instead focused on North Carolina, Ohio and Pennsylvania.

The Trump campaign has said future ad buys will target Virginia.

Republican strategist Ford O’Connor, who specializes in Virginia politics, said Mr. Trump’s struggles in the state go beyond demographics, though he stressed that the growth in Northern Virginia, which coincides with the growth of the federal government, is a major factor.

“Part of it is a demographic shift and part of it is Trump’s personality,” Mr. O’Connor said. “Who’s the group that he is underperforming with? Suburban affluent voters, which is what has grown the most in Virginia.”

Many Trump supporters echo their candidate’s disdain for the news media and blame bad press coverage for his low poll numbers in Virginia and nationally.

“The media, in my opinion, has become a propaganda tool for the Democrats,” said Sam Henley, 76, a retired financial manager in Fredericksburg.

In a move to counter negative coverage, Mr. Trump last week began using a scripted stump speech delivered with the aid of teleprompters, avoiding the off-the-cuff remarks that have distracted attention from his message.

At the rally, Mr. Trump made an appeal to every faction in Virginia: He promised law and order for suburban voters, jobs in coal country, support for agriculture and forestry industries, and health care reforms for the state’s large veteran population.

However, his most direct appeal was to black voters. The pitch has become a staple of his stump speech since he reorganized his campaign last week, but it took on added urgency in Virginia.

“The GOP is the party of Lincoln, and I want our party to be the home of the African-American vote once again. I want an inclusive country, and I want an inclusive party,” said the New York business mogul.

Attempting to turn the tables on Mrs. Clinton, who has labeled Mr. Trump a racist, he described the former first lady, U.S. senator and secretary of state as a political bigot.

“We reject the bigotry of Hillary Clinton, who sees people of color only as votes, not as human beings worthy of a better future,” he said. “We’ve seen what the Democratic policies have done in cities like Detroit, Baltimore and Chicago.”

Mr. Trump’s unconventional run already has managed to sway some Obama voters in Virginia.

Tammy Zacofsky, a 49-year-old baker, said she voted twice for Mr. Obama but switched her registration from Democrat to Republican because of Mr. Trump.

“I guess you could say he woke me up,” said Ms. Zacofsky, who joined thousands of fellow Trump fans for the rally at the Fredericksburg Expo Center.

She jokingly blamed her votes for Mr. Obama on “temporary insanity,” which she said Mr. Trump has cured.

“I started to see what’s happening with the country, and I’m not happy at all with the way it is headed,” she said. “I hope many people will open their eyes the way I did.”

She wasn’t the only one.

Independent voter Russell Peterson, 65, said he backed Mr. Obama in 2008 and 2012 but this year would vote for Mr. Trump over Mrs. Clinton.

“I’m worried that we are going to lose some of our rights if the Democrats get it,” he said.

He said Mr. Trump is making the right moves to turn the tide in Virginia.

“This is what it takes,” Mr. Peterson said outside the Expo Center. “He needs to be here.”

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