Ex-Obama adviser David Axelrod cautioned supporters of Kamala Harris against casting her as the default replacement to President Biden on the 2024 ticket, warning that she will need to prove to voters that she is capable of earning the nomination.

"I think the focus of many leaders in the party is going to be singular and it‘s going to be how and who can defeat Donald Trump and that may well be Kamala Harris," Axelrod said Sunday. "I think some of her supporters have done her a disservice because they say, well, she‘s there, she‘s historic, you can‘t bypass her and so on…

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"The real case they should be making is why she‘d be the strongest candidate. And there are some really strong arguments to suggest she would be, but she might be stronger if she comes through a process that is open, and I noticed in her own statement, she said she wanted to compete and earn the nomination, and it would be good for her if that was the conclusion that people drew," he added.

Kamala Harris dressed in all black holds mic during event

US Vice President Kamala Harris has been endorsed by President Biden as the nominee. (Leigh Vogel/Abaca/Bloomberg via Getty Images)

Axelrod made the comment on "CNN Newsroom" after he was asked why former President Obama notably failed to endorse Harris for the Democratic nomination in his statement reacting to news of Biden's suspended campaign.

Biden endorsed Harris moments after he announced his decision to drop out of the race. She confirmed that she would run for the Democratic nomination in a statement, writing that "I am honored to have the President’s endorsement and my intention is to earn and win this nomination."

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Harris has received endorsements from former President Clinton and former Secretary of State Hillary Clinton, as well as several Democratic lawmakers. However, many Democrats have issued statements on Biden's decision without making mention of Harris or endorsing her. 

"We will be navigating uncharted waters in the days ahead. But I have extraordinary confidence that the leaders of our party will be able to create a process from which an outstanding nominee emerges," Obama wrote in his statement.

Vice President Kamala Harris and President Joe Biden

President Joe Biden signs an executive order with US Vice President Kamala Harris during an event in the East Room of the White House in Washington, DC, on Monday, Oct. 30, 2023. (Al Drago/Bloomberg via Getty Images)

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Democrats believe that the vice president is in the best position to take on former President Trump with just months to the election. Several Democratic operatives told Fox News Digital that Harris was voted for by the same primary voters that chose Biden, and she has already established a campaign and fundraising infrastructure going into the crucial contest. 

But Axelrod said that mentality won't serve her well politically. 

"I think that people are going to take a hard look at this, try and open up the process and see if others step forward," he said. "Others may not, but she would be in a stronger position if she can say, I went through a process and I emerged as the nominee of the Democratic Party by dent of that process and not just as a gesture by the president to hand me he this nomination."

Then-Democratic presidential candidate former Vice President Joe Biden listens as then-Democratic vice presidential candidate Sen. Kamala Harris, D-Calif., speak at the Carpenters Local Union 1912 in Phoenix, Thursday, Oct. 8, 2020, to kick off a small business bus tour. (AP Photo/Carolyn Kaster)

Then-Democratic presidential candidate former Vice President Joe Biden listens as then-Democratic vice presidential candidate Sen. Kamala Harris, D-Calif., speak at the Carpenters Local Union 1912 in Phoenix, Thursday, Oct. 8, 2020, to kick off a small business bus tour. (AP Photo/Carolyn Kaster)

"She may be battle-scarred, but she‘s also battle-tested in a way others aren‘t and they should be making that case," he went on.

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Harris, for her part, hailed Biden's decision as a "selfless and patriotic act," adding that he is "doing what he has done throughout his life of service: putting the American people and our country above everything else." His decision to suspend his campaign comes after several weeks of mounting pressure following a poor debate performance last month, which promoted 37 congressional Democrats and those who caucus with them to urge Biden to drop out. 

Fox News' Julia Johnson contributed to this report.