WASHINGTON—Federal Bureau of Investigation Director James Comey on Thursday said a number of plots near the July 4 holiday by suspects inspired by Islamic State were disrupted by a spate of arrests, adding that law-enforcement officials are continuing to pursue leads as the militant group uses social media in a bid for followers.

Mr. Comey said “more than 10” people had been arrested in the past four weeks and they had links to the Islamic State militant group, though not all of them were charged with terrorism-related crimes.

“I do believe that our work disrupted efforts to kill people, likely in connection with July 4,” Mr. Comey told reporters during a briefing at FBI headquarters.

“The reason I say it that way is the nature of these guys,” he said. “It’s actually hard to figure out when they are trying to kill somebody.”

He didn’t provide details of the suspected plots, and didn’t say that they had been coordinated or directed by Islamic State militants overseas.