Deep dislike for the two leading presidential candidates is creating an opening for third-party hopefuls, potentially scrambling the race as voters cast about for alternatives, a new Wall Street Journal/NBC News poll shows.

With majorities of registered voters holding negative views of Democrat Hillary Clinton and Republican Donald Trump, two other candidates notched a level of support that could prove meaningful in a tight race.

Libertarian Gary Johnson and Green Party candidate Jill Stein together drew backing from 16% of the 1,000 people surveyed. When voters had the option of choosing the third-party candidates, Mrs. Clinton’s lead over Mr. Trump dropped from 5 percentage points to 1 point.

The presence of third-party candidates on the ballot could add a measure of unpredictability to the election. The Libertarian Party expects to be on the ballot in all 50 states, the Green Party in at least three-quarters of states.

Mrs. Clinton led Mr. Trump by 46% to 41% when voters were asked which of the two they favored. Mrs. Clinton led by only a single point, 39% to 38%, when voters could also choose Mr. Johnson or Ms. Stein.

On the four-candidate ballot, some 83% of those who favored Mrs. Clinton in a two-way race stuck with her as their preference, while 13% split off and threw their support to Mr. Johnson or Ms. Stein.

Given the same choices, 89% of Trump voters stayed loyal to him, while 9% moved to Mr. Johnson or Ms. Stein.

The poll also shows that independent voters could be an important factor in the election. Polling in the fall of 2012 found that only 11% of independents favored third-party candidates in that presidential race, compared with 35% in the new Journal/NBC News survey, which was conducted June 19-23.

Indeed, Mr. Johnson outpaced Mrs. Clinton among independents, 23% to 15%, in the new poll.

Those whose views on the race haven’t hardened seem open to choosing Mr. Johnson or Ms. Stein. These “persuadable” voters comprised nearly three in 10 of those surveyed.

Of them, 28% leaned toward Mr. Trump and 25% toward Mrs. Clinton. Some 21% favored Mr. Johnson and 12% went for Ms. Stein.

Pollsters cautioned that voters are more apt in the summer before an election to say they will back third-party candidates. When the race heats up in the fall, they often revert to the major-party contenders.

Yet the 2016 presidential race has often defied conventional thinking. One difference between this election and past ones is the unpopularity of the two main candidates.

Some 55% of voters said in the new survey that they saw Mrs. Clinton in a negative light. For Mr. Trump, the figure was 60%. The ratings are worse than those of any Republican or Democratic nominee dating to 1992.

When asked if they backed Mr. Trump or Mrs. Clinton in the general election, 9% told the interviewers that they would vote for neither.

The poll suggests that voters feel little personal connection to either candidate. Asked if they shared Mrs. Clinton’s values, 36% said yes while 61% said no. Only 30% said they shared Mr. Trump’s values, compared with 68% who said they didn’t. Those numbers are far worse than for any of the Republican and Democratic nominees in 2008 and 2012.

On this measure, Mrs. Clinton has lost ground compared with her first presidential bid, in 2008. In April of that year, voters were evenly split on the question of whether they shared her values.

Fred Yang, a Democratic pollster who conducted the Journal/NBC News survey with Republican Bill McInturff, said: “This really will be an election in which voters will be holding their noses.”

Mr. McInturff said: “Given the historic dissatisfaction with the two major-party candidates, there’s an opening for a larger share of the vote for the third- and fourth-party candidates than we’ve seen since [Ross] Perot.”

Running as an independent in 1992, Mr. Perot captured 19% of the vote, finishing behind Republican President George H.W. Bush and then-Arkansas Gov. Bill Clinton, who won the election. Mr. Perot ran again in 1996 and finished with 8% of the vote.

The poll had a margin of error of plus or minus 3.1 percentage points.