Election 2024 updates: Michelle Obama to speak at DNC this week

Rep. Ilhan Omar has won her Congressional primary in Minnesota, the Associated Press projected Tuesday night.

Omar's win follows defeats by two of her fellow squad members in their primaries – Cori Bush from Missouri, and Jamaal Bowman of New York.

Omar had been expected to win in her district despite a challenge from former Minneapolis city council member Don Samuels.

Bush lost her primary earlier this month to St. Louis County prosecutor Wesley Bell. He was backed by more than $8 million from the pro-Israel United Democracy Project.

Bowman lost to Westchester County Executive George Latimer in June. Per AdImpact, the race was the most expensive House primary on record, with most of the funding coming from the American Israel Public Affairs Committee’s (AIPAC) United Democracy Project PAC in support of Latimer. Latimer was recruited to run by AIPAC.

-ABC News' Tal Axelrod, Brittany Shephard and Oren Oppenheim

Minnesota Gov. Tim Walz, in his first solo campaign appearance, defended his military record and thanked his vice presidential opponent, Sen. JD Vance, for his service.

"I am damn proud of my service to this country," Walz said to applause at the AFSCME convention in California. "And I firmly believe you should never denigrate another person's service record. Anyone brave enough to put on that uniform for our great country, including my opponent, I just have a few simple words: thank you for your service and sacrifice."

Vance has repeatedly criticized how Walz has talked about his military record, which included 24 years in the Army National Guard before he retired to run for Congress in 2005. Vance served as a combat correspondent for four years in the U.S. Marine Corps.

Read more about Vance's comments and Walz's background here.

President Joe Biden on Tuesday, as he was departing the White House, said he would go to Trump's inauguration in January if he were to win this year's election.

"I have good manners, not like him," Biden told reporters after being asked if he'd attend. Trump did not attend Biden's inauguration in 2021.

Biden also defended his calling Trump "a genuine danger to American security," a comment he made during his CBS News interview over the weekend. Asked whether that contradicted his calls to cool heated political rhetoric, Biden shot back: "That's just a statement. That's a factual statement."

-Fritz Farrow

Independent presidential candidate Cornel West will be allowed on the general election ballot in North Carolina following a judge's ruling that reversed a decision that would have kept him off the ballot in the battleground state.

In a ruling on Monday, U.S. District Judge Terrence Boyle ordered the North Carolina State Board of Elections to certify Justice for All North Carolina as a political party in the state. That party, started by West's campaign, is nominating him as its candidate in North Carolina and some other states. The board had previously voted to deny certifying the party over concerns about how signatures were gathered for its petition to become a certified party.

Justice for All North Carolina called the decision a "monumental day for our party" but West's campaign still faces headwinds. The Democratic National Committee filed a complaint with the FEC alleging that West's campaign received "illegal In-Kind Contributions" from firms it used to collect signatures for ballot access petitions in Arizona and North Carolina -- allegations West has pushed back on.

"We've always said we're going to ensure the third party candidates are playing by the rules, and it's clear his campaign isn't playing by the rules," DNC spokesperson Matt Corridoni told ABC News after the complaint was filed.

-Oren Oppenheim