Florida Sen. Bill Nelson Clarence (Bill) William NelsonDemocrats sound alarm on possible election chaos Trump, facing trouble in Florida, goes all in NASA names DC headquarters after agency's first Black female engineer Mary W. Jackson MORE wants to require FBI notification if a suspected terrorist tries to buy a gun — even if the federal investigation has been closed.

The Democrat introduced legislation Wednesday, in the wake of the mass shooting in Orlando, requiring information about a terrorism probe by the Justice Department or other agency to be included in the National Instant Criminal Background Check System (NICS).

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Under Nelson's legislation, the NICS would then notify the FBI if an individual was previously — or is currently — the subject of a terrorism investigation tries to buy a gun.

“We’re not saying don’t sell guns to someone just because they were investigated,” Nelson said. “But having a system in place that alerts the FBI if someone they once investigated is suddenly trying to purchase multiple assault weapons is just common sense.”

Nelson's legislation comes after the Sunday massacre at a gay nightclub in Orlando, the deadliest mass shooting in U.S. history.

FBI Director James Comey told reporters earlier this week that gunman Omar Mateen had previously been investigated by the bureau and was on a federal watchlist for approximately 10 months in 2013 and 2014.

Nelson's legislation comes as the Senate is heading toward a larger fight over gun control.

Also on Wednesday, Sen. Chris Murphy Christopher (Chris) Scott MurphyDemocratic senator calls for 'more flexible' medical supply chain to counter pandemics The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon GOP chairman to release interim report on Biden probe 'in about a week' MORE (D-Conn.) took over the Senate floor in an extended speech calling for action on gun control over the Orlando shooting.

Democrats are pledging to force a vote on a proposal from Sen. Dianne Feinstein Dianne Emiel FeinsteinMcConnell says Trump nominee to replace Ginsburg will get Senate vote Top Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence Intensifying natural disasters do little to move needle on climate efforts MORE (D-Calif) aimed at blocking individuals on the terror watchlist from being able to buy guns or explosives.

Senate Republicans, however, argue the proposal is too broad and would sweep up Americans not tied to terrorism.

Instead, they're backing a proposal from Sen. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas) that would allow the attorney general to delay suspected terrorists from getting a gun for up to 72 hours as they try to get a court to approve blocking the sale of the firearm.