Illinois lawmakers are discussing measures to give the state more authority to stop people who threaten violence from buying guns after the deadly shooting this week at a July Fourth parade in Highland Park.

Suspected gunman Robert Crimo III, who has been charged with seven counts of murder, obtained a permit required in Illinois to buy guns after encounters with police in 2019 in which he attempted suicide and threatened to kill his family.

State Rep. Denyse Stoneback, a Democrat who represents the Chicago area, said the gunman’s past behavior should have barred him from buying firearms. “This is all extremely concerning,” said Ms. Stoneback, who is involved in the talks about drafting the new legislation. “There’s a lot we can do, and loopholes in the law which we need to fill.”

She said she and others in the Democratic-controlled legislature are discussing proposals including mandatory fingerprints for those seeking gun licenses and in-person background checks with local law enforcement agencies.