Joseph R. Biden Jr. appears to face limited political pressure from voters about whom to choose as his running mate, with no contender emerging as a clear favorite and the great majority of people saying that race should not be a factor in his decision, according to polling conducted by The New York Times and Siena College.

Mr. Biden has pledged to select a woman as his nominee for vice president, and his advisers are vetting more than half a dozen people for the job. In recent weeks, amid ongoing demonstrations against racism and police violence, a number of prominent Democrats have pressed Mr. Biden to select an African-American woman. And his search committee has been reviewing at least five black women, one Latina and one Asian-American candidate.

Earlier this month, Senator Amy Klobuchar of Minnesota, a white moderate, removed herself from consideration for vice president after sustained criticism of her record as a prosecutor, and she publicly urged Mr. Biden to put a woman of color on his ticket.

In the Times poll, four in five registered voters said that race shouldn’t be a factor in Mr. Biden’s selection of a running mate. That group included three-quarters of the black voters polled, and more than 8 in 10 white and Hispanic voters.

About a fifth of black voters said they would like to see Mr. Biden choose a black running mate. The largest group with that preference was very liberal voters, at 37 percent; 27 percent of voters with postgraduate degrees said the same.

The poll asked respondents if they thought Mr. Biden should chose a black running mate or a white running mate or if race shouldn’t be a factor. The poll did not ask about the possibility that Mr. Biden could choose a Latina or an Asian-American candidate, but he is seriously considering women of both backgrounds.

In the six most important battleground states, voters’ professed indifference to race was even stronger. Nine in 10 registered voters in those states said race should not be a factor in Mr. Biden’s choice of running mate, including 91 percent of black voters and 85 percent of Hispanics.

The polls had margins of sampling error of 1.8 percentage points in the battleground states and three percentage points nationally.

Mr. Biden’s eventual choice is certain to face intensive scrutiny, in part because of Mr. Biden’s age. If he is elected, Mr. Biden, currently 77, would be the oldest president ever on the day of his inauguration, and he would turn 80 about halfway through his term, a reality that worries some voters.

Mr. Biden has said he is looking for someone who shares his overall approach to governing and who would be prepared for the presidency “on Day 1.” He has also said he would prefer a running mate with strengths that complement his own, as well as someone who would be willing to challenge him rather than being cowed by the office of the presidency.

Follow-up interviews with poll respondents suggested that many voters are in tune with Mr. Biden’s stated approach.

“I don’t believe that the problems in America can be solved just by having, for example, a black president or a black vice president,” said Garfield Campbell, 54, of Scottsdale, Ariz., a poll respondent. Mr. Campbell, who is black, continued, “The right person has to be someone that can sort of counterbalance, or add value and strength, to Joe Biden, in areas where he may not be as strong.”

Mr. Biden’s wide lead over President Trump in national polls — he was ahead by 14 percentage points in a Times/Siena survey this week — could give him an unusually free hand in choosing a running mate: He is not desperately seeking a sidekick who could help him shake up the race, as John McCain did in 2008 when he put the charismatic but obscure Alaska governor, Sarah Palin, on his ticket. Nor is Mr. Biden confronting questions about his own readiness for the presidency, as Barack Obama did when he selected Mr. Biden.

Christine Matthews, a Republican pollster who has been critical of Mr. Trump, said that the political impact of Mr. Biden’s selection might be limited because he is so far ahead in the race.

“It matters less this year, because of his large lead and his appeal to fairly broad constituencies,” said Ms. Matthews, adding that her own view was that Mr. Biden ought to choose a black woman.

Yet the size and diversity of Mr. Biden’s emerging coalition presents delicate dynamics of its own, as his choice of running mate may well excite one element of his political base at the cost of upsetting another.

Of the women known to be under consideration, only a few have prominent national profiles. None of the better-known women appeared in the poll to be a runaway favorite with voters.

Senator Elizabeth Warren of Massachusetts was the best-known contender, and she was seen favorably by 45 percent of registered voters and unfavorably by 42 percent. Ms. Warren inspired the strongest reactions of any candidate tested in the poll, with three-fifths of very liberal voters saying they had a very favorable view of her and an equal share of very conservative voters expressing a strongly negative view. A majority of moderate voters had a somewhat or very favorable opinion of her.

In the swing states, Ms. Warren’s favorability rating was evenly split, with 41 percent of people saying they had a favorable view and the same share saying the opposite.

Ellen Schiffman Adelstein, 78, of Tucson, said she admired Ms. Warren’s work on consumer protection matters but worried that her positions on issues like health care were too far to the left, posing a risk to the ticket if Mr. Biden selected her.

“I want a new president,” Ms. Schiffman Adelstein said. “I don’t want anything to mess up getting a new president in there.”

But Khalil Skerritt, 30, of Tallahassee, said that Ms. Warren would push Mr. Biden to move urgently on promises of structural reform.

“She’ll be the one to be like, ‘No, we have four years to get stuff done,’” said Mr. Skerritt, who supported Bernie Sanders in the Democratic primary.

Senator Kamala Harris of California, another well-known candidate in the vetting process, had similarly mixed numbers, with 40 percent of voters expressing a favorable view and 35 percent seeing her unfavorably. Two-thirds of black voters had a positive impression of Ms. Harris, a few percentage points better than Ms. Warren.

Ms. Harris was somewhat less well known in the battleground states and showed few pronounced points of strength or weakness there. Thirty-five percent of swing-state voters said they had a favorable view of her, and 30 percent said the opposite.

The public was far less familiar with two other black women under consideration: Representative Val Demings of Florida, a former police chief who is among the most serious vice-presidential prospects, was unknown to 4 in 5 voters both nationally and in her expansive home state. Stacey Abrams, the former Georgia governor candidate, was seen favorably by about a third of registered voters nationwide but was unknown to nearly half.

Allison Bryan-Harris, 41, of Eagle Lake, Fla., said she planned to cast an unenthusiastic vote for Mr. Biden — “I could vote for a box at this point,” she said — but expressed excitement about Ms. Abrams, calling her “forward-thinking” and “progressive.”

Wilfredo Torres, 71, a Hispanic military retiree from Charlotte, N.C., favored Ms. Demings for vice president, saying he believed “it’s a good time to have somebody African-American on the ticket.” He also said her law enforcement experience was an asset.

Two white women from the Midwest who have spoken with Mr. Biden’s vetting team, Senator Tammy Baldwin of Wisconsin and Gov. Gretchen Whitmer of Michigan, drew positive marks in their home states, suggesting that either could be well positioned to help Mr. Biden cement his lead in a key battleground.

But Mr. Biden is already leading both of those states by substantial margins, and it is not clear that he needs help from a running mate to lock up a local victory.

A third Midwesterner, Senator Tammy Duckworth of Illinois, who is Asian-American, was also unknown to most voters.

Elaine Meyer, of Detroit, spoke highly of Ms. Whitmer. But she added, “I don’t want to lose her as governor.” A 41-year-old white librarian, she said she hoped Mr. Biden would choose a black woman as his running mate.

Ms. Meyer said she had seen Mr. Biden speak in person and found him to be “engaging” and “very competent.” But she said she still found his age “a little worrisome.”

Voters showed no interest in the idea that he could pledge to serve just one term as president, a possibility briefly debated by some of Mr. Biden’s advisers early in the presidential race.

Eighty-five percent of registered voters nationwide said a one-term pledge would make no difference in their decision to vote for or against Mr. Biden.

Rebecca Wabish, a Biden supporter in New Hanover, Pa., said it was plain enough to her that Mr. Biden would be a one-term president. For that reason, Ms. Wabish, 67, said she hoped he would ensure there was “strong leadership coming up behind him.”

“You don’t have to look so far in the future: He’ll never make it through a second term because of his age,” Ms. Wabish said. “I think what he has to do is get a very, very strong V.P.”

Here are more results and our explanation of the methodology for the poll.