"It will be looked at and reviewed carefully before any action or any decision is made," Twito said.
Baugh has said he does not intend to resign, but "deserved to be chastised" for his comments about the victim.
The judge also said during Monday's sentencing hearing that Moralez had as much control of the situation as Rambold.
He later told reporters that what he said was wrong, irrelevant to the case, demeaning of women and not reflective of his beliefs.
Baugh was first elected to the bench in 1984 and has been re-elected every six years since without an opponent. Originally from Texas, he is the son of legendary NFL quarterback Sammy Baugh of the Washington Redskins.
He said he has not decided whether to run again in 2014 but has no intention of resigning.
Baugh said the sentence was based on Rambold's violation of an earlier deal he made with prosecutors, rather than the original crime. He plans to file a further explanation for the sentence with the court.
"The public doesn't exactly understand how that came about," Baugh said, adding that it's not unusual in his experience for people to disagree with criminal sentences.
One of the organizers of Thursday's rally, Sheena Rice, said protesters will seek to defeat Baugh if he runs again.
The rally packed the courthouse lawn with hundreds of people, many carrying signs such as "Justice for Cherice" and "14 is 14."
Joining in the backlash against the judge was Montana's Democratic governor, Steve Bullock, who said Baugh's comments "made me angry." But Bullock added that he has no authority over the judge and any complaints against him would be handled by the state Judicial Standards Commission.