WASHINGTON—Vice President Kamala Harris declared that her “values have not changed” on key issues such as climate change and immigration despite shifting policy stances , as she and her running mate, Minnesota Gov. Tim Walz , sat for their first major television interview of their 2024 campaign Thursday.

Harris and Walz, who have faced criticism that they have avoided close media scrutiny, spoke to CNN’s Dana Bash as they took a bus tour through Georgia. Harris addressed questions regarding fracking and other areas where her position has changed and defended President Biden’s economic record, but didn’t lay out significant new details on how she would govern if elected to the White House this fall.

Asked what she would tackle on day one, she pointed to previously announced efforts to cut housing costs and offer tax credits for families.

“People are ready for a new way forward,” Harris said.

The interview came a week after Harris’s Chicago convention and as polls have shown her in a competitive position against former President Donald Trump in more than a half-dozen battleground states. The interview came ahead of the Labor Day holiday, which marks the start of the fall presidential campaign. Harris will be in Michigan and Pennsylvania on Monday, while Trump will be in Pennsylvania on Friday.

Trump responded to the interview on his social-media platform, saying: “BORING!!!” He added: “I look so forward to Debating Comrade Comrade Kamala Harris and exposing her for the fraud she is.”

Fracking, immigration and Gaza

During her earlier campaign for president that kicked off in 2019, Harris said she was in favor of banning fracking, a stance backed by environmentalists, but has since disavowed that position. Pressed on that shift in the interview Thursday, Harris said she had made clear in 2020 that she wouldn’t ban fracking. That year, she said in the vice-presidential debate that she agreed with Biden’s energy plan, which didn’t include a fracking ban.

“What I have seen is we can grow and we can increase a thriving green energy economy without banning fracking,” she said Thursday.

Asked about immigration, Harris pointed to her credentials as a former California attorney general who had prosecuted transnational criminal organizations who trafficked guns, drugs and human beings. “We have laws that have to be followed and enforced that address and deal with people who cross our border illegally, and there should be consequences,” Harris said.

Harris has sought to strike a balance on immigration policy that would “create an earned pathway to citizenship and secure our border,” as she said in last week’s convention address, along with her vow to bring back the border-security bill that failed in the Senate and sign it into law. She had previously struck a softer tone on illegal migrant crossings.

Asked about Biden’s work to end the war in Gaza, Harris stuck close to the president’s position, calling on Israel and Hamas to reach an agreement on a cease-fire and an exchange of hostages. “We have to get a deal done,” she said.

Praise for Biden

Harris said that she had just served pancakes and was sitting down to do a puzzle with her grand nieces when Biden called her on July 21 to say he was getting out of the race.

“I asked him ‘are you sure’ and he said ‘yes,’ ” Harris said. She said that while Biden was clear he would support her, “my first thought was not about me, to be honest with you. My first thought was about him.”

She argued that Biden’s presidency would be judged favorably. “I think history is going to show that in so many ways it was transformative,” she said.

Still, she didn’t answer directly when asked if “Bidenomics” was a success. She cited the administration’s work, including reducing the cost of prescription drugs for seniors, and said: “I’ll say that that’s good work. There’s more to do, but that’s good work.”

A Republican cabinet pick?

Harris, who has said she would serve as president for “all Americans,” said in the interview that she would appoint a Republican to her cabinet if she wins the White House. She didn’t, however, offer potential names.

“I think it’s important to have people at the table when some of the most important decisions are being made that have different views, different experiences. And I think it would be to the benefit of the American public to have a member of my cabinet who was a Republican,” Harris said.

Past presidents have appointed lawmakers of the opposing party to their cabinet: Republicans Chuck Hagel of Nebraska and Ray LaHood of Illinois served in the Obama administration, while George W. Bush chose Norman Mineta, a California Democrat, to serve as his Transportation secretary.

Questions about Walz’s past statements

Walz was pushed to address questions about some of his past statements on his military record and his family’s use of fertility treatments.

The Minnesota governor served for 24 years in the National Guard. He recently drew pushback over a 2018 clip that showed him speaking out against gun violence. “We can make sure those weapons of war, that I carried in war, are only carried in war,” he said. Critics seized on the comment, noting that he didn’t serve in combat.

Walz said he was proud of his service. “I think people are getting to know me,” he said. “I wear my emotions on my sleeves, and I speak especially passionately about our children being shot in schools and around guns. So I think people know me. They know who I am.” Of other missteps, he said, “I certainly own my mistakes when I make them.”

Write to Ken Thomas at ken.thomas@wsj.com and Catherine Lucey at catherine.lucey@wsj.com