President Obama has refrained from endorsing Vice President Harris, saying that the Democratic Party will select an “outstanding nominee.”

“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,” Mr. Obama said in a statement.

“I believe that Joe Biden’s vision of a generous, prosperous, and united America that provides opportunity for everyone will be on full display at the Democratic Convention in August. And I expect that every single one of us are prepared to carry that message of hope and progress forward into November and beyond,” he said.

Concerns are growing among some Democrats that Ms. Harris may weaken the party’s chances against President Trump in the upcoming election. Mr. Obama’s significant influence among Democrats means his lack of endorsement could harm Ms. Harris’s candidacy and potentially encourage other contenders to emerge.

Before Mr. Biden dropped out, there was speculation that it would be difficult to bypass Ms. Harris — a Black woman — and pick another replacement. Yet Mr. Obama, as America’s first Black president, could help sell a choice other than Ms. Harris.

A prominent voice among left-wing Democrats, Congresswoman Alexandria Ocasio-Cortez, disclosed in a TikTok video that those advocating for Mr. Biden to step down also wish to see Ms. Harris removed from the ticket.

“I’m gonna’ say what a lot of these folks aren’t saying… If you think that there is consensus among the people who want Joe Biden to leave, that they will support Vice President Harris, you would be mistaken,” she said. “I’m going to be honest for them. I’m in these rooms… a lot of them are not just interested in removing the president, they are interested in removing the whole ticket.”