Sen. Bernie Sanders, Vermont independent, has gained some ground against former Secretary of State Hillary Rodham Clinton over the past few months in the race for the 2016 Democratic presidential nomination, though Mrs. Clinton still has a firm grasp on the top spot, according to a new poll.

Mrs. Clinton was the first choice of 51 percent of Democrats and Democratic-leaning voters in the new survey from Monmouth University — down from 57 percent in June and 60 percent in April.

Mr. Sanders was well back at 17 percent, but his numbers have increased since his 7 percent showing in April and his 12 percent support in June.

Former Maryland Gov. Martin O’Malley and former Sen. Jim Webb of Virginia were both at 1 percent, while former Rhode Island Gov. Lincoln Chafee registered no support and 15 percent said they were undecided.

Vice President Joseph R. Biden Jr., who unlike the other candidates has not yet officially indicated his 2016 plans, was at 13 percent, with an additional 12 percent of Democratic voters saying they would be very likely to consider supporting Mr. Biden if he enters the race and another 31 percent saying they would be somewhat likely to consider it.

Among those who say they’d be likely to support Mr. Biden if he runs, 68 percent are Clinton backers, 18 percent are supporting another candidate and 14 percent are undecided.

“Most people seem to be focusing on a Sanders surge among the liberal wing of the party. But the bigger threat to Clinton may come from a Biden candidacy, where the two would be fighting for the same voters,” said Patrick Murray, director of the independent Monmouth University Polling Institute.

A slight majority, 53 percent, said it would be better if Mrs. Clinton faced an active primary challenge, compared to 36 percent who said it would be better if the party got behind Mrs. Clinton early on.

Seventy-four percent of Democratic voters held a favorable opinion of Mrs. Clinton, compared to 17 percent who held an unfavorable view.

Mr. Biden had a 67 percent/17 percent favorable/unfavorable split among Democrats, while Mr. Sanders had a 36 percent/12 percent split.

Fewer than 30 percent of Democrats had an opinion on the rest of the field.

The survey taken from July 9-12 of 1,001 adults had a subset of 357 registered voters who identified as Democrats or leaning Democratic, with a margin of error of plus or minus 5.2 percent for that subgroup.

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