ANNAPOLIS, Md. — With Maryland’s governor term-limited, the highly competitive contest to replace Larry Hogan has drawn the attention of President Trump, Speaker Pelosi, and even Oprah Winfrey.

As voters on Tuesday choose nominees in statewide, legislative, and congressional races, the pivotal governor’s race takes top billing. Mr. Hogan, a rare two-term Republican governor in a Democratic-leaning state, won plaudits from both sides of the aisle for his bipartisan approach and his willingness to challenge Mr. Trump.

His legacy on the line, Mr. Hogan has endorsed Kelly Schulz in the Republican gubernatorial primary. Ms. Schulz, who served as labor and commerce secretaries in Mr. Hogan’s administration, faces a challenge from Dan Cox, a Trump-backed state legislator who sued Mr. Hogan over his pandemic policies and later sought unsuccessfully to impeach him.

On the Democratic side, a former U.S. labor secretary and Democratic Party chairman, Tom Perez, has the backing of Ms. Pelosi, a native daughter of Baltimore, while author Wes Moore has clinched the support of Ms. Winfrey and Representative Steny Hoyer, the No. 2 House Democrat. Other top candidates include Comptroller Peter Franchot, a former attorney general, Doug Gansler, and a former U.S. education secretary, John B. King Jr.

The big-name endorsements that have rolled into Maryland’s primary elections for governor illustrate the high stakes for both parties. Democrats see the contest as one of their best chances nationwide to flip a governor’s mansion in this year’s midterm elections, while Republicans want to cement the party’s hold on the office.

The Republican primary provides a potential 2024 preview of the appeal of candidates in the mold of Messrs. Hogan and Trump, who offer competing visions for the future of the party.

Other top races in Tuesday’s election include contests for U.S. Senate, U.S. House, and attorney general. A Democratic senator, Chris Van Hollen, is facing a primary challenger two months after suffering a minor stroke, but is expected to easily win renomination. The state’s eight-member congressional delegation has an open seat representing a district in the Washington suburbs. The daughter of the state’s former attorney general is vying for her father’s old job.

It could take days, or even longer, to determine the winners in the most closely contested races. That’s because Maryland law prohibits counties from opening mail ballots until the Thursday after election day.

In all, 10 candidates are on the ballot for the Democratic nomination for governor. Mr. Perez has support from labor unions around the state, while Mr. Moore, the former CEO of the Robin Hood Foundation, an anti-poverty organization, has been endorsed by the state’s teachers union and the two top leaders of the Maryland general assembly, the house speaker, Adrienne Jones, and the senate president, Bill Ferguson.

Mr. Franchot, who has won four statewide races by wide margins to be the state’s tax collector, brings significant name recognition to the primary. Mr. Gansler, a longtime prosecutor, is running as a moderate. Mr. King served in President Obama’s Cabinet.

Voter Laura Kretchman, a 41-year-old high school teacher, said Mr. Moore’s endorsement by the Maryland State Education Association helped her decide to cast her ballot for him. She said she’s impressed by what Mr. Moore has accomplished after rising above childhood challenges and being raised by a single mom.

“I teach children at a school that also come from difficult upbringings, so I’d like to see maybe what he can bring to helping those students that are struggling and challenged,” Ms. Kretchman, an Annapolis resident, said.

While Mr. Moore has highlighted his credentials outside of government, some voters said they preferred a long resume of government service. For that reason, a 67-year-old voter in Annapolis,  Curtis Fatig, said he settled on Mr. Perez, who also worked on the Montgomery County council, as Maryland’s secretary of labor, and as the assistant attorney general for civil rights in Mr. Obama’s administration.

“He’s not a newcomer,” Mr. Fatig, who also likes that Mr. Perez has union support, said.

In the Republican primary for governor, Mr. Hogan has stood firmly behind Ms. Schulz, whom he sees as the strongest candidate to go up against a Democrat in November. Democrats seem to agree, with the Democratic National Committee plowing more than $1 million behind an ad intended to boost Mr. Cox in the Republican primary. It’s a tactic the Democrats have used in other states in an effort to face an easier opponent in the general election.

Mr. Hogan has criticized Mr. Cox for organizing busloads of Trump supporters to go to Washington on January 6, 2021, for the “Stop the Steal” rally that preceded the riot at the U.S. Capitol. Mr. Cox has said he didn’t go to the Capitol and left before the rioting began.

In a tweet he later deleted, Mr. Cox called Vice President Pence a “traitor” for refusing to heed Mr. Trump’s demands not to certify the 2020 election. He apologized for it and denounced the attack on the Capitol.

Mr. Trump, meanwhile, has branded Ms. Schulz and Mr. Hogan as RINOs, or Republicans In Name Only, a term of derision reserved for party members who don’t fall in line behind him.

“Get rid of Shutdown RINO Larry Hogan who is trying to get another RINO into office, Kelly Schulz,” Mr. Trump said in a statement late Monday.

Maryland’s only open congressional seat is in the 4th Congressional District, a heavily Democratic Black-majority district in the suburbs of the nation’s capital. Representative Anthony Brown is leaving his safe seat to run for attorney general. A former representative who previously held the seat, Donna Edwards, is running to get her job back and faces a former county prosecutor, Glenn Ivey, in Tuesday’s Democratic primary.

The Democratic primary for attorney general has turned into a battle between the wife of a former governor, Katie Curran O’Malley, who is a former Baltimore judge and the daughter of a former attorney general, and Mr. Brown, a former lieutenant governor who lost the 2014 governor’s race to Mr. Hogan.

The two are vying to replace the Democratic attorney general, Brian Frosh, who is retiring. Maryland hasn’t had a Republican attorney general in nearly 70 years.

In other races, candidates are on the ballot for all 188 seats in the Maryland general assembly, which is controlled by Democrats.

The Maryland primary was delayed by three weeks by the state’s highest court because of lawsuits challenging the state’s congressional and state legislative maps.

By Brian Witte