U.S. Sen. David Vitter said Friday he is looking at options to reduce the number of criminals who commit subsequent offenses and at bolstering the state’s mental health system as part of his criminal justice strategy as he seeks the Governor’s Mansion.

Those issues, as well as ways of keeping a State Police presence in New Orleans, were discussed during a closed-door forum the Metairie Republican held with criminal justice experts at the New Orleans Convention and Visitors Bureau. Vitter spoke with reporters after the session.

One idea, which Vitter said he is only just starting to think about, would involve tying the reimbursements the state pays to local jails to house state prisoners to metrics that track how well local officials are doing at preventing recidivism.

The state also should look at ways of strengthening its mental health services, Vitter said. While he offered few details, he pointed to St. Tammany Parish, where officials teamed up with a private company to run a psychiatric hospital after it was closed by Gov. Bobby Jindal’s administration during a round of budget cuts.

Vitter also came out in support of a continued State Police presence in New Orleans, saying it is a good short-term solution for a department that has too few officers on the streets. That assistance, however, should not come out of the State Police budget, he said, endorsing the current arrangement in which tourism officials have provided $2.5 million to support the troopers’ presence in the city.

“I think a lot of folks’ feeling in the city is that there needs to be a short-term solution,” Vitter said.

The forum is one of several Vitter has been holding across the state in the run-up to the 2015 governor’s race. The forums, described by Vitter and his aides as opportunities to discuss major policy issues facing the state, are off-limits to the media, though the senator has held brief discussions with reporters after the events.

Lt. Gov. Jay Dardenne and Public Service Commissioner Scott Angelle, both Republicans, and Democratic state Rep. John Bel Edwards, of Amite, also have announced for governor.

The idea of criminal justice reform, with a focus on keeping offenders from returning to jail, clashes with the traditional view of many Republicans supporting strict punishments and long sentences. However, showing concern about issues with the criminal justice system could help Vitter connect with leaders in the black community who have pushed for similar approaches.

Being able to win over some black voters could pay off for Vitter if he faces a runoff against Angelle or Dardenne, who are seen as being better able to draw support from both parties in a head-to-head match-up with the senator.

The meeting drew an eclectic list of attendees, including New Orleans District Attorney Leon Cannizzaro and Orleans Parish Sheriff Marlin Gusman, both Democrats. Also present were State Police Superintendent Col. Mike Edmonson, advocates for mental health and crime prevention, representatives of the tourism industry, former local FBI Chief Jim Bernazzani and former U.S. Attorney Jim Letten.

The event did not include any members of New Orleans Mayor Mitch Landrieu’s administration or the New Orleans Police Department. Vitter said Landrieu was invited but declined.

Landrieu’s name is often floated as a potential Democratic candidate for governor, though there has been little evidence that he is preparing to enter the race.

Follow Jeff Adelson on Twitter, @jadelson.