A House special election primary in Cleveland on Tuesday is shaping up as a proxy war over the direction of the Democratic Party, with the top two candidates drawing millions in donations as prominent figures including Sen. Bernie Sanders and Rep. James Clyburn line up on opposing sides.

Nina Turner, a top surrogate for Mr. Sanders (I., Vt.) during his presidential campaigns, has long been the front-runner in the race, which includes 13 candidates. The former state senator, 53 years old, who backs liberal plans including Medicare for All and the Green New Deal, has raised $5.6 million since announcing her candidacy, according to her campaign.

Her top rival, Cuyahoga County Councilwoman Shontel Brown, 46, has proved tough competition. She has raised $2.4 million, according to her campaign, and drawn the support of not only Mr. Clyburn, the powerful House Democratic whip from South Carolina, but also former Secretary of State Hillary Clinton, who defeated Mr. Sanders in the 2016 presidential primary.

Ms. Brown has said she would support Medicare for All and a Green New Deal if they came up for a vote, but she also would back more gradual approaches.

Tuesday’s primary will determine the Democratic nominee for the special election Nov. 2 to fill the seat vacated by Marcia Fudge, who left Congress earlier this year to run the Department of Housing and Urban Development. The district which includes Cleveland, its eastern suburbs and part of Akron, is solidly Democratic and whoever wins the primary this week is expected to prevail in the fall.

Rep. James Clyburn has described Cuyahoga County Councilwoman Shontel Brown as a deal maker.

Rep. James Clyburn has described Cuyahoga County Councilwoman Shontel Brown as a deal maker.

Photo: Michael M. Santiago/Getty Images

The contest is the most expensive House race of the year so far, according to OpenSecrets.org. It has gotten increasingly heated, with Ms. Turner in a recent ad questioning Ms. Brown’s ethics. In an ad in May, Ms. Brown pitched herself as someone who would work with President Biden, saying, “That’s different than Nina Turner.”

Messrs. Sanders and Clyburn held dueling events Saturday to pitch their candidates. “I see, in Shontel Brown, Marcia Fudge all over again,” said Mr. Clyburn, describing her as a deal maker. “Nina Turner will fight alongside of me,” Mr. Sanders said about Ms. Turner and her support of liberal policies.

The race comes as the Democratic Party is feeling the strains between its more progressive wing and its more centrist establishment. Those tensions played out in the Democratic presidential primary when Mr. Biden, helped by an endorsement by Mr. Clyburn, defeated Mr. Sanders. While liberals picked up several House seats in 2020, the progressive candidate lost a special election runoff in April for a House seat in Louisiana, and this year’s Democratic primary races for Virginia governor and New York mayor both went to centrists.

Ms. Brown said in an interview she always expected the race to have an outsize footprint because of Ms. Turner’s prominent roles in Mr. Sanders’s campaigns, and she welcomes the attention and fundraising it brings.

“What we’ve found there are some folks that are pleased to know there’s an alternative,” said Ms. Brown, who is also the chairwoman of the Cuyahoga County Democratic Party. She has attempted to contrast her local record with that of Ms. Turner, who spent the last two election cycles on the road for Mr. Sanders.

Shontel Brown, who is also the chairwoman of the Cuyahoga County Democratic Party, has raised $2.4 million, according to her campaign.

Shontel Brown, who is also the chairwoman of the Cuyahoga County Democratic Party, has raised $2.4 million, according to her campaign.

Photo: Da'Shaunae Marisa for The Wall Street Journal

“It doesn’t change how or why we are running, we’ve always run a local race. I’ve been here for the last nine consecutive years,” said Ms. Brown.

Ms. Turner, meanwhile, is going for a two-track approach: welcoming the energy of the progressive movement while trying to remind voters that she has also been a longtime presence in the community.

“Voters know me and my record of public service inside this district,” Ms. Turner said in an emailed interview. “While the media may like to frame this race as a battle for the future of the party, the truth is that we progressives are already the future.”

She has welcomed visits to the district from Mr. Sanders and other supporters including Rep. Alexandria Ocasio-Cortez (D., N.Y.). However, Ms. Turner, who has been critical of Mr. Biden, has also been playing up her support for former President Barack Obama. In one ad, she highlighted that she was twice an Obama delegate to the Democratic National Convention.

The Ohio district is racially and economically diverse. It is majority African-American but also includes the state’s largest population of Jewish Americans. Income levels vary widely, from high levels of poverty in East Cleveland where average annual income was under $21,000, to nearby Beachwood where the average income was more than $89,000, according to 2019 Census figures.

Former Ohio state Sen. Nina Turner has raised $5.6 million, according to her campaign.

Former Ohio state Sen. Nina Turner has raised $5.6 million, according to her campaign.

Photo: Michael M. Santiago/Getty Images

In an interview, Mr. Sanders said Ms. Turner, who was a co-chair of his 2020 campaign, “is the kind of intelligence and energy we need here in the United States Congress.” He dismissed the notion that the result of the race would signal the direction of the party: “Every time there’s an election, you guys go through this whole routine again: We lose an election, we’re collapsing; we win an election, we’re soaring.”

Mr. Clyburn, who has pitched Ms. Brown as the right person to carry on the legacy of those who have held the seat before, also played down whether the outcome would carry a broader meaning for the party. “I don’t think so, any more than I think the recent mayoral election in New York sent a symbol that the Democratic Party is moving to the right,” he said referring to Eric Adams, who won the New York Democratic mayoral primary.

State Rep. Janine Boyd, who represents Cleveland Heights, has endorsed Ms. Turner, even though she doesn’t identify with the Sanders-aligned wing of the party. She said Ms. Turner’s experience as a state senator and city councilwoman is what sold her, along with her willingness to compromise, including with former Gov. John Kasich, a Republican.

“I’m a bit of a policy nerd so that’s just how I looked at it,” she said.

Shaker Heights City Councilman Rob Zimmerman said he is working to build support for Ms. Brown, whom he said he identifies with politically and stylistically.

He said he is also concerned by past comments from Ms. Turner critical of Israel. During the conflict earlier this year between Israel and Hamas, Ms. Turner retweeted activists saying they stood with Palestinians and using the hashtag #EndApartheid. She has also said she opposes unconditional aid to Israel, unlike Ms. Brown.

“I would prefer that my member of Congress, that their default position, would be supportive of Israel,” Mr. Zimmerman said.

Pro-Israel group Democratic Majority for Israel has funded ads for Ms. Brown.

Ms. Turner said she supports a two-state solution for Israelis and Palestinians that ensures peace and security.

Write to Eliza Collins at eliza.collins+1@wsj.com.