In a tweet on Tuesday, South Dakota Gov. Kristi Noem, a Republican, said she believes Ravnsborg, also a Republican, should resign.
She added the state will release additional materials related to the investigation into the September crash that killed Joseph Boever.
House Majority Whip Tim Goodwin, R-Rapid City, has also said he thinks Ravnsborg should resign, but notes lawmakers could force him out of office through impeachment, the Argus Leader reports.
"So what's best for the citizens of South Dakota? My recommendation is that our Attorney General needs to do the honorable thing and resign his post," Goodwin wrote in a letter to his constituents, according to the paper. "He needs to do it immediately so we as a state can move forward."
Lawmakers had said they were considering starting the impeachment process earlier this week, and by Tuesday Rep. Will Mortenson, a Republican, had filed an article of impeachment.
The Argus Leader says South Dakota's Constitution allows lawmakers to impeach a constitutional officer for various reasons, including misdemeanors.
Ransborg was charged last week with three misdemeanors – using a mobile device while driving, careless driving and a lane violation – in connection to a Sept. 12 crash that killed Boever.
Officials said Boever was walking along the shoulder of Highway 14 near Highmore when Ravnsborg veered onto the shoulder and fatally struck him around 10:30 p.m.
Initially, Ravnsborg thought he hit a deer and said he helped the sheriff search for what he hit that night, but didn't find anything. Hyde County Sheriff Mike Volek let Ravnsborg take his personal vehicle home.
When Ravnsborg was driving to return the sheriff's vehicle the next day, he discovered Boever's body on the side of the road and then drove to the sheriff's house to tell him, Ravnsborg explained days after the fatal crash.
A spokesperson for Ravnsborg told the Argus Leader earlier this week he "does not intend to resign."
If lawmakers do move forward with impeaching Ravnsborg, it would mark the first formal impeachment proceeding in South Dakota history, the paper notes.