The contours of the race remain relatively unchanged, according to the CNN poll. Mrs. Clinton continues to hold large leads with women, minorities and voters with college degrees. Mr. Trump does best with men, white voters and those who did not go to college.

On issues, Mr. Trump is seen as the strongest candidate to manage the economy and handle terrorism, while Mrs. Clinton wins on foreign policy and has an edge on immigration.

Voters view Mr. Trump as being the more honest candidate, but they prefer Mrs. Clinton’s temperament when it comes to being best suited to be commander in chief. Last week, Mr. Trump engaged in a Twitter spat with the president of Mexico, raising questions about his ability to deal with other world leaders.

But Mr. Trump, who has been moderating his positions recently, has also gained an advantage over Mrs. Clinton when it comes to appealing to independent voters. Nearly half of those queried say they would vote for the Republican nominee, while 29 percent say they would vote for Mrs. Clinton.

Although the poll does not indicate whether Mr. Johnson is pulling voters from either candidate, his supporters tend to be younger and more highly educated — suggesting that they would be more likely to be potential backers of Mrs. Clinton.