LOS ANGELES, June 24 (Reuters) - Hawaii's governor signed a bill making it the first state to place its residents who own firearms in a federal criminal record database and monitor them for possible wrongdoing anywhere in the country, his office said.

The move by gun control proponents in the liberal state represents an effort to institute some limits on firearms in the face of a bitter national debate over guns that this week saw Democratic lawmakers stage a sit-in at the U.S. House of Representatives.

Hawaii Governor David Ige, a Democrat, on Thursday signed into law a bill to have police in the state enroll people into an FBI criminal monitoring service after they register their firearms as already required, his office said in a statement.

Click through images from the 2016 Democratic sit in for gun control:

9 PHOTOS 2016 Democratic sit in for gun control See Gallery 2016 Democratic sit in for gun control A photo shot and tweeted from the floor of the U.S. House of Representatives by U.S. House Rep. Katherine Clark shows Democratic members of the House staging a sit-in on the House floor "to demand action on common sense gun legislation" on Capitol Hill in Washington, United States, June 22, 2016. U.S. Rep. Katherine Clark/Handout via Reuters. A photo shot and tweeted from the floor by U.S. House Rep. Rep. John Yarmuth shows Democratic members of the U.S. House of Representatives, including Rep. Joe Courtney (C) staging a sit-in on the House floor "to demand action on common sense gun legislation" on Capitol Hill in Washington, United States, June 22, 2016. REUTERS/ U.S. Rep.John Yarmuth/Handout A photo shot and tweeted from the floor of the House by U.S. House Rep. David Cicilline shows Democratic members of the U.S. House of Representatives, including Rep. John Lewis (R) staging a sit-in on the House floor "to demand action on common sense gun legislation" on Capitol Hill in Washington, United States, June 22, 2016. REUTERS/ U.S. Rep. David Cicilline/Handout A photo tweeted from the floor of the U.S. House by Rep. Donna Edwards (R) shows Democratic members of the U.S. House of Representatives, including herself and Rep. John Lewis (L) staging a sit-in on the House floor "to demand action on common sense gun legislation" on Capitol Hill in Washington, United States, June 22, 2016. REUTERS/Rep. Donna Edwards/Handout A photo shot and tweeted from the floor of the House by U.S. House Rep. John Yarmuth shows Democratic members of the U.S. House of Representatives, including Rep. Joe Courtney (L) and Rep. John Lewis (C) staging a sit-in on the House floor "to demand action on common sense gun legislation" on Capitol Hill in Washington, United States, June 22, 2016. REUTERS/U.S. Rep. John Yarmuth/Handout UNITED STATES - JUNE 22: House Minority Whip Steny Hoyer, D-Md., center left, speaks with Rep. John Lewis, D-Ga., center right, as House Democrats rally on the House steps to speak about gun legislation on Wednesday, June 8, 2016. Also pictured are Rep. Jim Langevin, D-R.I., left, and Rep. Paul Tonko, D-N.Y. Democrats were staging a sit-in on the House floor in an attempt to force a vote on gun legislation in the House of Representatives. (Photo By Bill Clark/CQ Roll Call) UNITED STATES - JUNE 22: Rep. Bobby Rush, D-Ill., flanked by House Minority Leader Nancy Pelosi (D-CA) and Dan Gross, president Brady Campaign to Prevent Gun Violence, speaks about his family's experience with gun violence as House Democrats rally on the House steps to speak about gun legislation on Wednesday, June 8, 2016. Democrats were staging a sit-in on the House floor in an attempt to force a vote on gun legislation in the House of Representatives. (Photo By Bill Clark/CQ Roll Call) UNITED STATES - JUNE 22: Sen. Richard Blumenthal (D-CT) left, and Sen. Chris Murphy (D-CT) speak to reporters after leaving the House floor on Wednesday, June 8, 2016. The two senators joined House Democrats who were staging a sit-in on the House floor in an attempt to force a vote on gun legislation in the House of Representatives. (Photo By Bill Clark/CQ Roll Call) Representative Jeb Hensarling, a Republican from Texas and chairman of the House Financial Services Committee, makes an opening statement during a hearing with Janet Yellen, chair of the U.S. Federal Reserve, not pictured, in Washington, D.C., U.S., on Wednesday, June 22, 2016. By offering a subtle change to her outlook from less than a week ago, Yellen on Tuesday before the Senate Banking Committee pushed the prospect of additional interest rate increases further into the future. Photographer: Andrew Harrer/Bloomberg via Getty Images Up Next See Gallery Discover More Like This HIDE CAPTION SHOW CAPTION of SEE ALL BACK TO SLIDE

The Federal Bureau of Investigation database called "Rap Back" will allow Hawaii police to be notified when a firearm owner from the state is arrested anywhere in the United States.

Hawaii has become the first U.S. state to place firearm owners on the FBI's Rap Back, which until now was used to monitor criminal activities by individuals under investigation or people in positions of trust such as school teachers and daycare workers

"As you can imagine, the NRA finds this one of the most extreme bills we've ever seen," said Amy Hunter, a spokeswoman for the National Rifle Association's institute for legislative action.

The law could affect gun owners outside Hawaii, because the state requires visitors carrying guns to register, Hunter said.

As a result, they could be added to "Rap Back" because they arrived in the state with a gun, she said. The Hawaii attorney general's office said a weapon-carrying visitor should be able to petition for removal from the national database after leaving the state.

Hawaii state Senator Will Espero, a Democrat who co-authored the law and owns a gun, called it "common sense legislation that does not hurt anyone."

The law, which takes effect immediately, allows police in Hawaii to evaluate whether a firearm owner should continue to possess a gun after being arrested.

"It just means local police will be notified," Espero said in a phone interview.

Ige's office said he also signed into law two other firearms bills. One makes convictions for stalking and sexual assault among the criminal offenses disqualifying a person from gun ownership. The other requires firearm owners to surrender their weapons if diagnosed with a mental, behavioral or emotional disorder. (Reporting by Alex Dobuzinskis; Editing by David Gregorio and Ed Davies)

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