WASHINGTON—Vice President Kamala Harris secured the pledged support of a majority of delegates to the Democratic National Convention on Monday, putting her on track to formally lock up the party’s nomination next month to take on former President Donald Trump this fall.

To secure the nomination, Harris needed a majority of the 3,949 pledged delegates to the convention, which begins Aug. 19, who can vote on the first ballot. By Monday evening, Harris had secured more than 2,200 delegates, giving her enough to claim the nomination, according to a count by the Associated Press.

Harris traveled to Wilmington, Del., to meet with campaign staff based in President Biden’s hometown, and Biden, who is recuperating from Covid-19 , called into the gathering. He said he realized it was difficult for many staff members to learn of his decision but “it was the right thing to do.”

“The name has changed at the top of the ticket, but the mission hasn’t changed at all,” Biden said, according to audio piped into the event.

Harris, joined by second gentleman Doug Emhoff, thanked staff members at the campaign office, telling them, “I know it’s been a roller coaster and we’re filled with so many mixed emotions about this.” Harris noted that she had asked Biden campaign chair Jen O’Malley Dillon and campaign manager Julie Chavez Rodriguez to stay on in their roles, adding, “I have full faith that this team is the team that will be the reason we win in November.”

Harris noted the applause for Biden and asked the president on the phone if he was watching the event. “I’m watching. I’m watching,” Biden said. “You’re the best, kid.” Biden outlined a list of unfinished business, telling the campaign staff, “I’m still going to be fully, fully engaged. I’ve got six months left in my presidency, I’m determined to get as much done as I possibly can.”

Biden’s statements at the campaign event Monday were his first public comments since he isolated because of Covid-19 last week.

The president is scheduled to return to the White House Tuesday afternoon, the White House said.

Harris vowed to win the election as she consolidated support from delegates who will determine the nomination at next month’s Democratic National Convention in Chicago. State party delegations from Florida, North Carolina and Tennessee announced plans to support the vice president, a strong showing that gives her a leg up over any challengers who might emerge .

As of Monday, Harris was running unopposed .

Sharif Street, the Pennsylvania Democratic Party chair, expressed confidence Harris would receive firm support from his state’s delegates. “I’ve talked to state chairs from across America and I have seen nothing but overwhelming support for the vice president,” Street said. “I overwhelmingly believe our delegation, and delegations throughout the country and commonwealth will support Kamala Harris.”

Harris continued to rack up endorsements from across the Democratic Party, winning the backing of governors such as Wes Moore of Maryland, Gretchen Whitmer of Michigan, J.B. Pritzker of Illinois and Andy Beshear of Kentucky. Those endorsements, from officials who had been floated as potential replacement nominees, clear a path for Harris to lock up the nomination without much resistance.

Former House Speaker Nancy Pelosi (D., Calif.) offered her support, saying she had “full confidence that she will lead us to victory in November.”

“I have seen Kamala Harris’s strength and courage as a champion for working families, notably fighting for a woman’s right to choose,” Pelosi said.

House Democratic Leader Hakeem Jeffries (D., N.Y.) told reporters that he and Senate Majority Leader Chuck Schumer (D., N.Y.) would meet with Harris “shortly” but he stopped short of issuing an endorsement.

Harris earned her first labor endorsement from the American Federation of Teachers, the union of 1.8 million members who are holding their convention in Houston. “Talk to your co-workers. Talk to your neighbors. Knock on doors. Write postcards. Put out the lawn sign and slap on the bumper sticker,” said Randi Weingarten , the union’s president. “We can’t risk regretting we didn’t do more.”

That endorsement was followed by the support of the AFL-CIO, which represents 60 unions and 12.5 million workers.

Biden remained in Rehoboth Beach, Del., recovering from Covid-19, leaving Harris to attend an official event at the White House celebrating the National Collegiate Athletic Association championship teams from the 2023-2024 season. Harris, in her first appearance since Biden said he wouldn’t seek re-election , praised the president’s record at the South Lawn ceremony, calling his accomplishments “unmatched in modern history.”

Later, at the event at the campaign headquarters, Harris offered a glimpse of a hard-edge stump speech challenging Trump, pointing out that as a prosecutor she “took on perpetrators of all kinds. Predators who abused women. Fraudsters who ripped off consumers. Cheaters who broke the rules for their own gain. So hear me when I say, I know Donald Trump’s type.”

The Trump campaign criticized Harris as more liberal than Biden.

“A vote for Kamala is a vote to continue inflation, open borders, high gas prices, and war around the world,” said Karoline Leavitt, the Trump campaign’s national press secretary.

In Ohio, Trump’s running mate , Ohio Sen. JD Vance, made only fleeting references to Biden or Harris at his first solo rally. Harris “is our vice presidential candidate officially, but I guess she’s gonna run for president now,” Vance said, prompting scattered boos from the crowd.

“When I see her give a speech, and she talks about the history of this country, [it’s] not with appreciation but with condemnation,” said Vance.

Vance said he had been looking forward to debating Harris in a vice-presidential debate, but she will likely debate Trump instead. “I’m kind of pissed off about that, if I’m being honest with you,” Vance joked.

Harris’s campaign appeared to energize voters and big donors alike. In the first 24 hours since Biden’s departure from the race, the Harris campaign and the DNC and joint fundraising committees raised $81 million.

Future Forward, the Democratic super political-action committee that was supporting Biden’s bid, said it had received commitments of $150 million in the 24 hours since Biden dropped out and backed Harris. The surge came from contributors who had previously withheld donations, or hadn’t been committed to giving to the organization, according to a senior aide with the super PAC.

Once Harris locks down the nomination, as expected, she will need to pick a running mate. Some of the early contenders included North Carolina Gov. Roy Cooper, Arizona Sen. Mark Kelly, Pennsylvania Gov. Josh Shapiro, and Beshear of Kentucky. Harris held separate calls with Shapiro, Cooper and Beshear, according to people familiar with the calls.

The new Harris campaign has requested vetting materials, including financial records and family histories, from several potential running mates, including Cooper, Kelly and Shapiro, according to a person familiar with the process. The campaign has also requested vetting information from Whitmer, Minnesota Gov. Tim Walz and Pritzker, the person said.

Whitmer, however, said she didn’t want to be considered for the role. “I am not leaving Michigan. I am proud to be the governor of Michigan,” Whitmer told the Detroit News on Monday.

Beshear said in an interview with CNN that he had “not been personally asked to submit information at this point.”

The Democratic National Committee said it would adopt rules Wednesday allowing for a virtual nomination of their presidential ticket ahead of the Chicago convention and that process would be completed between Aug. 1 and an Aug. 7 Ohio deadline for ballot access.

While the Aug. 7 deadline has been theoretically removed by a measure signed into law in the state, it doesn’t go into effect until September. DNC officials said they could face litigation, which could put at risk their presidential nominee’s ability to be at the top of the ticket in Ohio.

“There is still a need for a virtual component to our nominating process. That has not changed,” said Minyon Moore, the convention chair. “We will not allow technicalities or MAGA extremists to obstruct the electoral process.”

To receive the nomination, candidates need to be qualified Democrats, qualified to be U.S. president and have the support of at least 300 convention delegates, with no more than 50 coming from any one state delegation. Officials said the process would give the nominee the flexibility to choose a vice presidential candidate before ballot-access deadlines beginning in August.

Write to Ken Thomas at ken.thomas@wsj.com