On his first day in office, George Gascón, the district attorney of Los Angeles, said that taking a fresh look at long prison sentences handed down during the high-crime 1990s would be a centerpiece of his agenda as a progressive prosecutor.

His office, he said at his swearing-in ceremony almost four years ago, would work to “correct the injustices of the past.”

On Thursday, Mr. Gascón tried to do just that. At a packed news conference, he announced that he would ask a court to resentence Lyle and Erik Menendez, who are serving a life sentence without the possibility of parole after killing their parents in 1989 in the living room of the family’s Beverly Hills mansion.

The petition could pave the way for the brothers to walk free, decades after their case captured the attention of the American public in one of the first trials broadcast to the nation on television.

Today, Mr. Gascón is fighting for re-election in a tough race that has him far down in the polls, as many voters express support for a more punitive approach to prosecuting crime and question whether Mr. Gascón’s lenient, reform-driven policies have made Los Angeles less safe.

One of Mr. Gascón’s last major acts in office could very well be helping the Menendez brothers secure their freedom.