Former Rep. Jim Moran, D-Va., a longtime congressman from Northern Virginia, said on "This Week" that he believes Northam should not resign.
Late Friday, Northam issued an apology and acknowledged that he had appeared in the photo, though he did not specify whether he was the individual in blackface or the KKK robe and hood. "I think the constitutional provisions are very specific on the succession of office".
If Northam stepped down, Lt. Gov. Justin Fairfax would be the second African-American governor in Virginia's history.
Northam worshipped at his home church, the predominantly black First Baptist in Capeville, but otherwise kept out of sight on Sunday as calls intensified for him to step down.
Northam came under fire Friday when a photo from his 1984 medical school yearbook page surfaced.
Even if Northam doesn't resign, the scandal threatens to cripple his ability to govern. In running for governor, many people - including the 87 percent of black voters who supported him - saw Northam as a candidate who belongs to a party associated with justice and equality, who ran against an opponent tied to a president who has been accused of racism.
"I winced when I saw that", former Gov. Terry McAuliffe said on CNN. "That was not Ralph Northam". "If Ralph is watching this today, I know how much he loves this commonwealth of Virginia, and you've got to make the right decision".
In a statement on Saturday, Fairfax said he was "shocked and saddened" by the picture but was glad Northam, whom he called a friend, had apologised and reached out to him personally for "actions from his past" that he could not condone. But a day later, he denied he was in the photo, while also acknowledging he once put on blackface to imitate Michael Jackson at a dance contest in Texas decades ago.
Northam initially released statements on Friday, saying he regretted his decision to be in the photo and apologizing.
"Inappropriate circumstances", she reportedly told him.
In addition to the Monday meeting, Northam also met with his staff in an emergency meeting Sunday after pressure from Democrats to resign. Northam said he recognizes now that was wrong.
"My first intention. was to reach out and apologise", he said, adding that he recognised that people would be offended by the photo.
The origins of blackface date to 19th-century "minstrel" shows in which white performers covered their faces in black grease paint to caricature slaves.
"You know how this church survived through 1880 and through lynchings and through firebombings and through all this stuff?"
Referring to the allegation against him, Fairfax said he was not surprised it came at a critical time: "It's at that point that they come out with the attacks and the smears". We have to close that chapter. "We have to move Virginia forward". "We have a leader that thinks their personal ambitions is more important than the good of the state". He grew up on the eastern shore, the most rural and remote portion of the state, and he followed a career path steeped in conservative traditionalism: Virginia Military Institute, medical school followed by an eight-year stint as an Army doctor, then 15 years in a lucrative private practice as a pediatric neurologist in the Norfolk area.
She pointed out how Northam had been previously scrutinized over his support for a bill that would repeal restrictions on third-trimester abortions.