Democratic presidential nominee Hillary Clinton is opening a wider lead in three battleground states, while maintaining an advantage over Republican rival Donald Trump in Florida, a new Wall Street Journal/NBC News/Marist poll has found.

In Colorado, Mrs. Clinton leads Mr. Trump by 14 percentage points, 46% to 32%—six points more than a poll taken in July before the two parties held their national conventions.

Mrs. Clinton also gained some ground in two Southern battleground states: Virginia, where she leads 46% to 33%, and North Carolina, where she is ahead 48% to 39%.

In Florida, one of the most important states this fall with its 29 Electoral College votes, the race is tighter. Mrs. Clinton’s support stands at 44%, compared with 39% for Mr. Trump, which is a slight improvement in his position from a month ago, when the poll had him trailing 2 points further behind.

Still, even winning Florida in November wouldn’t help Mr. Trump if his fortunes don’t improve in the other battlegrounds. North Carolina is a state that Mitt Romney won in 2012, and Colorado and Virginia have been trending Democratic in presidential elections. Democrats’ position in Virginia is also likely enhanced by Mrs. Clinton’s selection of the state’s popular junior senator, Tim Kaine, to be her running mate.