Robert F. Kennedy Jr. is polling stronger than any third-party candidate has in decades, pulling in roughly 10 percent of registered voters across the battleground states as he saps support from both President Biden and former President Donald J. Trump, a new series of polls has found.

The overall results in the Biden versus Trump contest were virtually unchanged when Mr. Kennedy was included in the polls conducted by The New York Times, Siena College and The Philadelphia Inquirer. But beneath the surface of that seeming stability, the surveys revealed how Mr. Kennedy, powered by social media and younger voters, has emerged as an unpredictable X factor in what would otherwise be a 2020 rematch.

With less than six months until the election, the faction of the electorate giving Mr. Kennedy early support exposes some of the vulnerabilities inside the president’s Democratic coalition. Mr. Biden dropped all the way to 33 percent in a five-candidate race, an alarmingly low share of the vote for an incumbent president. The series of polls focused on what are expected to be the most contested states this fall: Arizona, Georgia, Michigan, Nevada, Pennsylvania and Wisconsin.