Voters are now more likely to credit Vice President Kamala Harris than Donald J. Trump with representing change and caring about people like them, as Ms. Harris takes a slim lead nationally in the race for the White House, according to the latest New York Times/Siena College poll.

The finding is the first time Ms. Harris has led Mr. Trump in the Times/Siena poll since July, when President Biden dropped out of the race and Democrats rallied behind Ms. Harris as his replacement. It comes as the contest moves into its final month, and surveys from the battleground states find the race to be one of the closest in modern history.

While the Times/Siena poll shows some solid advantages for Mr. Trump, the results suggest Ms. Harris is making gains, if small ones, on questions about temperament, trust and change that can be critical in a presidential race.

The poll, conducted from Sept. 29 to Oct. 6 among 3,385 likely voters, found that Ms. Harris led Mr. Trump, the Republican, by 49 percent to 46 percent, a slight lead that is within the poll’s margin of error.