• California Democratic Rep. Adam Schiff urged President Joe Biden to exit the 2024 presidential election contest.
• Schiff in a statement said that he had "serious concerns about whether the President can defeat Donald Trump in November."
• "While the choice to withdraw from the campaign is President Biden's alone, I believe it is time for him to pass the torch," said Schiff, the Democratic nominee for a U.S. Senate seat from California.

California Democratic Rep. Adam Schiff on Wednesday urged President Joe Biden to exit the 2024 presidential election contest.

Schiff in a statement said that he had "serious concerns about whether the President can defeat Donald Trump in November."

"While the choice to withdraw from the campaign is President Biden's alone, I believe it is time for him to pass the torch," said Schiff, the Democratic nominee for a U.S. Senate seat from California who is a strong favorite to win in November.

"And in doing so, secure his legacy of leadership by allowing us to defeat Donald Trump in the upcoming election," said Schiff, who is a close ally of Rep. Nancy Pelosi, the powerful California Democrat who previously served as House speaker.

A source familiar with Pelosi told CNBC on Wednesday that Schiff's statement was "news to her" and that he "did not consult her before."

But Schiff did notify Biden's campaign about the statement before releasing it to media outlets, a source told NBC News.

Politico on Tuesday reported that Pelosi has offered to talk to members of Congress who wanted to discuss their concerns about having Biden as the Democratic nominee.

In an interview last week on MSNBC's "Morning Joe," Pelosi refused to endorse Biden as the nominee, saying "It's up to the president to decide if he is going to run ... We're all encouraging him to make that decision because time is running short."

Schiff's statement came a day after The New York Times reported that he had warned Democratic donors during a meeting Saturday in Long Island, New York, that the party would be likely to lose its existing majority in the Senate and fail to gain control of the House of Representatives if Biden is the presidential nominee.

"I think if he is our nominee, I think we lose," Schiff reportedly told donors.

Schiff is one of the most prominent Democrats to publicly call on Biden to exit the race on the heels of the president's disastrous debate performance in late June against Trump, the Republican nominee.

Biden has been adamant since that debate in saying he will not drop out, despite concerns that his mental acuity has deteriorated during his three years in the White House. The president last week said he would not abandon his candidacy unless polls show "there's no way you can win," adding, "No poll shows that."

Schiff in his statement said that Biden "has been one of the most consequential presidents in our nation's history," and that the president's "lifetime of service as a Senator, a Vice President, and now as President has made our country better. 

"But our nation is at a crossroads," Schiff said. "A second Trump presidency will undermine the very foundation of our democracy, and I have serious concerns about whether the President can defeat Donald Trump in November."

The lawmaker added, "But make no mistake, whoever our party ends up nominating, or if the nomination remains with the president, I will do everything I can to help them succeed."

"There is only one singular goal: defeating Donald Trump," he said. "The stakes are just too high."

In response to CNBC's request for comment on Schiff's statement, the Biden campaign pointed to recent statements the president has made in response to similar calls for him to quit the contest.

In one of those statements, Biden said. "I wouldn't be running again if I did not absolutely believe I was the best person to beat Donald Trump in 2024."

In another of those statements, the president said, "Any weakening of resolve or lack of clarity about the task ahead only helps Trump and hurts us. It is time to come together, move forward as a unified party, and defeat Donald Trump."

- Additional reporting by CNBC's Kevin Breuninger