MANASSAS PARK, Va. — The high-stakes race for governor of Virginia entered its final stretch with Glenn Youngkin and Terry McAuliffe trading accusations of sowing division, as voters appeared closely divided over returning a Democrat to office or electing a Republican to lead their state for the first time in more than a decade.

The size and atmosphere of dueling events during the last weekend of campaigning before Election Day on Tuesday reflected the trends in the most recent polls. Mr. Youngkin, the Republican candidate, greeted crowds of more than 1,000, while Mr. McAuliffe, the Democrat, hustled through sparsely attended events from morning to night.

Mr. McAuliffe, who served one term as governor from 2014 to 2018, has displayed a rising sense of urgency lately, dispatching some of the Democratic Party’s biggest stars to campaign for him and push people to vote early. In 11 hours on Saturday, Mr. McAuliffe traveled more than 120 miles, making eight stops in six cities amid a whirlwind day of campaigning in which he urged supporters not to be complacent.

“We are substantially leading on the early vote, but we cannot take our foot off the gas,” Mr. McAuliffe told a crowd on Saturday in Norfolk, where he met with labor leaders who were planning to spend the day knocking on doors.

He and his allies took it as an encouraging sign that more than 1.1 million of Virginia’s 5.9 million registered voters had cast ballots as of Sunday morning, according to the Virginia Department of Elections.

But the energy this weekend was more palpable among Mr. Youngkin and his supporters, who have heeded the Republican’s calls for a new direction in the state’s political leadership after more than a decade of Democratic governors. Mr. Youngkin has framed the election as an opportunity for Virginians to send a message to the nation that Democrats are out of step with the majority of Americans on a number of issues, from how racial inequality is taught in schools to coronavirus-related mandates.

“The nation’s eyes are on Virginia,” Mr. Youngkin told an energetic crowd of several hundred people who came to see him on Saturday afternoon in Manassas Park, a city near the suburban Democratic stronghold of Fairfax County outside Washington. In his speeches, he often ascribes a larger significance to his campaign, saying, “This is no longer a campaign. It’s a movement.”

It was clear in interviews with voters over the weekend that many Virginians view this election as something symbolically greater than a face-off between two candidates for governor. The contest has exposed the country’s persistent divisions over questions of race, class, privilege and the appropriate role of government, and become an outlet for Virginians to register their dissatisfaction with the political culture.

“I’m a Hillary-Biden voter,” said Glenn Miller, a lawyer from McLean, as he walked into a Youngkin rally in southern Fairfax County on Saturday night that drew more than 1,000 people. He explained his tipping point: Working from home and hearing his teenage daughter’s teacher make a comment during a virtual lesson about white men as modern-day slaveholders.

“There are a lot of people like me who are annoyed,” he said, adding that he was able to vote for Mr. Youngkin because he did not associate him as a Trump Republican. “My problem with Trump was I thought he was embarrassing. I just don’t think Youngkin is going to embarrass me or the state.”

The McAuliffe campaign has tried to portray Mr. Youngkin as a Trump acolyte, accusing him of exaggerating fears that children are being divided by race by teachers who are encouraging them to see white people as inherently bad.

“He’s got parents fighting parents and parents fighting teachers,” Mr. McAuliffe said over the weekend. “He’s turned our school boards into war zones. It’s all about this critical race theory, which is not taught in Virginia. This is all he talks about. It has never been taught in Virginia. Let’s call it what it is: It’s a racist dog whistle. He’s run a racist campaign from start to finish.”

Some Democratic voters said they appreciated the link Mr. McAuliffe was making between former President Donald J. Trump and Mr. Youngkin, who opposes abortion, same-sex marriage and mandates for the coronavirus vaccine.

“I see a lot of issues with what’s going on in the national Republican Party,” said Jerry Dalesandro, 59, a retiree from Virginia Beach. “I’m a Biden fan, an Obama fan, but also more just a not-a-Trump fan.”

Mr. Youngkin has tried to strike a balance between keeping Mr. Trump close but not too close. The former president recently announced he would speak at a telephone town-hall-style event for Mr. Youngkin on Monday. But the Republican candidate said he would not be participating.

For Mr. McAuliffe, the visit to Norfolk was one of several stops he made in southeastern Virginia, where he drew small to modest crowds of 30 to 100 people. The largest crowd on Saturday was at a Black church in Portsmouth, where Mr. McAuliffe was joined by Representative Jim Clyburn of South Carolina, the civil rights leader.

President Biden, Vice President Kamala Harris and former President Barack Obama have all visited Virginia as part of the McAuliffe campaign’s push to boost turnout, especially among core Democratic constituencies such as Black voters. But generating enthusiasm has been difficult at times, which was evident on Saturday at a McAuliffe event in Chesapeake. When Mr. McAuliffe went to speak, the crowd yelled “Terry, Terry, Terry” only after a campaign staffer started the chant to ramp up the energy in the room.

On the minds of many Democrats was the unpleasant memory of what happened in 2016, when they believed Hillary Clinton was all but certain to win the White House. “You need to remember back how you felt in November of 2016, when we woke up and we realized who was going to be our next president,” Gov. Ralph Northam, who is prohibited from running again because of term limits, told a crowd in Virginia Beach on Saturday. “We do not want to wake up on November the 3rd of this year and have that same feeling.”

At the Youngkin events, it was unclear how many people were voters like Mr. Miller, the former Biden supporter now voting for the Republican. Many said they were committed Republicans, and the crowds were more diverse than Republican events typically are.

In the Washington suburb of Chantilly, John and Linda Torres of Herndon stood in a parking lot as the crowd of several hundred returned to their cars after a Youngkin rally. Ms. Torres held a Youngkin yard sign and a handful of stickers that read “Latinos for Youngkin.”

The couple said they both voted for Mr. Trump, but also for Mr. Obama. They said they disliked Mr. McAuliffe’s stance on vaccine mandates as well as his insistence that Mr. Youngkin was making a problem where one doesn’t exist by criticizing how race is taught in some schools. “I know some people say, ‘Oh, it’s all made up.’ But it’s real,” said Mr. Torres, 41, a veteran.

Ms. Torres, 43, a nurse, said she and her husband have considered pulling their two children out of public school and putting them into a Christian one. And that same impulse applied to her views on the state’s political leadership.

“We just want it to change,” Ms. Torres said.