Scott Peterson's Ex-Lawyer Mark Geragos 'Gratified' Innocence Project On the Case

The fact Scott Peterson's case has been taken up by the L.A. Innocence Project could result in the convicted murderer getting a new trial ... and his former attorney couldn't be happier.

Mark Geragos, Peterson's lawyer during his 2004 trial, joined us Friday on "TMZ Live," and we asked him about the startling development -- Innocence Project lawyers citing "new evidence" in court filings obtained by ABC News.

Mark says he feels "gratified" to have another set of eyes looking over Scott's case ... and also cites Peterson's reduced sentence as just one of many reasons the case needs more review.

Peterson's death sentence -- for murdering his wife Laci Peterson and their unborn child -- was knocked down to life without parole after the California Supreme Court said some jurors were improperly dismissed during jury selection.

Geragos says a hearing was ordered at the same time as the resentencing, and he thinks that's what drew the Innocence Project's attention  ... plus, Mark says the case against Scott is an "abomination."

Geragos says he can debunk all of the evidence from Peterson's trial, but thinks the jury was laser focused on Peterson's admission he was cheating on his wife.

The Innocence Project is a nonprofit that works to exonerate people who've fallen victim to wrongful conviction -- something Peterson has maintained is the case since the beginning.

The org confirmed it's repping Peterson, and added it's "investigating his claim of actual innocence" -- though they haven't elaborated beyond that.

In the court filing, the L.A. Innocence Project claims Peterson's state and federal constitutional rights were violated and his claim of actual innocence "is supported by newly discovered evidence."

As you may know ... Laci was 8 months pregnant with Peterson's child when she disappeared on Christmas Eve 2002. Her body was found in the San Francisco Bay months later.

Peterson became a prime suspect when it was revealed he was having an affair with his massage therapist, and cops arrested him in April 2003. He was found guilty of first-degree murder and second-degree murder.

ABC says the Innocence Project's asking for a ton of items related to the case it couldn't find ... including Laci's watch, evidence from a 2002 burglary across the street from the Petersons' home, and interviews with several witnesses.

The Stanislaus County D.A.'s Office, which prosecuted Peterson, says, "Mr. Peterson, like all individuals convicted of crimes, is afforded the legal right to appeal his conviction with representation of his choosing."