The F.B.I. is examining numerous metal fragments found near the stage at a campaign rally in Butler, Pa., to determine whether an assassin’s bullet — or potential debris — grazed former President Donald J. Trump’s head, bloodying his ear, according to the F.B.I. and a federal law enforcement official.

The bureau has asked to interview Mr. Trump as part of its broader investigation, hoping to provide insights into the shooting and possibly a more complete record of his injury, the official said, speaking on the condition of anonymity to discuss the continuing inquiry.

Unanswered questions about the object that struck the Republican nominee for president have lingered since the shooting on July 13, with Mr. Trump claiming that he was struck by a bullet — and casting his survival as an act of divine intervention.

F.B.I. officials have been more circumspect, citing the need to analyze the evidence before determining what struck Mr. Trump — a bullet, metal shard or something else.

The bureau’s shooting reconstruction team “continues to examine evidence from the scene, including bullet fragments, and the investigation remains ongoing,” the F.B.I. said in a statement on Thursday. In addition to injuring Mr. Trump, the gunman, Thomas Crooks, 20, of Bethel Park, Pa., shot three rally attendees, one fatally.

Steven Cheung, a Trump campaign spokesman, did not answer whether the bureau had asked to review the former president’s medical records after the incident, but Mr. Trump has not released them publicly.