Northam said he had been especially affected by a conversation with a black lawmaker, whom he declined to name, on the topic of blackface.
"If these accusations are determined to be true, I don't think he's going to have any other option but to resign", said Northam, who told King that he has not spoken to Fairfax since the second accuser went public Friday afternoon.
Other congressional Democrats made unqualified calls for Fairfax to resign.
Watch the complete interview Monday starting at 7 a.m. "CBS This Morning".
That's a question the state of Virginia has been grappling with since last week when its governor, Ralph Northam, was caught up in a row over blackface: the crude caricaturing of African Americans as a means of entertaining white people since the minstrel shows of the 1830s.
Allegations of sexual assault and rape lodged within the last week by two women against Virginia Lt. Gov. Justin Fairfax, a Democrat who is next in line for the top job, have complicated the political calculus surrounding Northam's fate. Herring - who would become governor if both Northam and Fairfax resign - had previously called on Northam to resign and came forward after rumours about the existence of a blackface photo of him began circulating at the Capitol.
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In a U.S. state key to defeating Donald Trump at the next Presidential election, the top three officials, all Democrats, have been embroiled in damaging scandals involving blackface and sexual assault.
Dr. Vanessa Tyson, a professor at Scripps College, accused Fairfax of sexually assaulting her in 2004 while they were both working at the Democratic National Convention.
Mr Fairfax denied the allegations and said he was the victim of a smear campaign. I also plan to reach out to our colleges and universities and talk about sensitivity training.
Northam said he supports an investigation, but stopped short of calling for Fairfax's resignation.
The governor has ignored calls to resign since a racist photo from his 1984 medical school yearbook surfaced.
The sit-down with CBS was the Democratic governor's first television interview since a racist photo in his 1984 medical school yearbook emerged on February 1, prompting leading Democrats to call for Northam's resignation.
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He said he had been in more hard situations in his medical career, and continued: "Right now, Virginia needs someone that can heal. And so again, I regret that our attorney general is in this positio, but this is a decision that he's going to need to make".
Northam said now is the time to take action and to employ government policies to address racial inequalities in the state.
So far, they've resisted repeated calls from around the nation to resign.
Almost 60 percent of African-Americans in Virginia want Gov. Ralph Northam to remain in office despite the recent scandal surrounding a racist photo on the Democrat's 1984 medical school yearbook page, according to a poll released Saturday. The governor acknowledged blackening his face later in 1984 to look like pop singer Michael Jackson for a dance contest he won.
The top three Democrats in Virginia's state government are now contending with various controversies, including Gov. Ralph Northam and state Attorney General Mark Herring admitting to having worn blackface in the 1980s.
But he also made another faux pas.
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