The Biden campaign sent out a pair of memos on Wednesday — one to staff members and another to Congressional Democrats — attempting to quell concerns about President Biden’s struggling re-election effort as a growing chorus of Democrats publicly vented its frustrations and fears that he could lose in November.

The memos, obtained by The New York Times and first reported by Politico, highlighted internal polling that showed a close race between Mr. Biden and Donald J. Trump, as well as Mr. Biden’s strong June fund-raising.

“Our internal battleground toplines from last night show a steady race: we estimate that we’re down just 1 point in margin,” Jennifer O’Malley Dillon, the Biden campaign chair, and Julie Chavez Rodriguez, the campaign manager, wrote in the memo to campaign staff members. “All of this is well within the margin of error.”

Mr. Biden’s stumbling performance in the presidential debate last week set off panic among Democrats about whether he should continue in the race. Two House Democrats have publicly said they believe Mr. Biden will be defeated in November. Another called for him to drop out of the race.

And even stalwart allies like Representative Nancy Pelosi of California, the former Speaker, and Representative Jim Clyburn of South Carolina, who continue to back Mr. Biden, have entertained questions about his candidacy, with Ms. Pelosi calling it “legitimate” to ask if his performance was a one-time flub or “a condition.” Mr. Clyburn said he would back Vice President Kamala Harris if Mr. Biden stepped aside.

On Wednesday, a White House official denied a New York Times report that Mr. Biden had told an ally he was considering dropping out.

The memos represented an attempt to quiet those fears as Mr. Biden prepared to campaign in Wisconsin on Friday and Pennsylvania on Sunday, two crucial battleground states. They were also notably more measured in tone than a fund-raising message from the campaign last week that referred to those calling for the president to drop out as the “bedwetting brigade.”

Both memos linked to a new television ad that the campaign debuted on Wednesday. And they urged Mr. Biden’s supporters to stay the course, even if his public polling should worsen.

“If we do see changes in polling in the coming weeks, it’s a moment in time and not a reshaping of the race,” Hillary Beard, a Biden campaign official, wrote in the memo to Congressional allies.

Several Democrats have said they were offended by how the campaign had previously dismissed their concerns.