"We stand with Democrats across Virginia and the country calling him to immediately resign", they wrote.
Many leading politicians, including House Speaker Nancy Pelosi, had urged the governor to "do the right thing" after the photo emerged.
The Republicans join a growing chorus of elected officials in Virginia and elsewhere calling for Northam's resignation.
During an interview on January 30 on WTOP-FM, he said that killing children after they were born could be an option under a new bill that Democrats are trying to pass in Virginia, The Epoch Times reported.
"When I was confronted with the images yesterday, I was appalled that they appeared on my page but I believed then and now that am not either of the people in that photo".
"I am simply asking for the opportunity to demonstrate beyond a shadow of a doubt that the person I was is not the man I am today", Northam said. "After I did that, I had a chance to reach out to classmates and my roommates and I am convinced, that's not my picture".
"I spoke with Governor Northam this morning".
But the Democrat who spoke to Northam said that after further reflection the governor said he has no memory of wearing either of the racist costumes and doesn't believe he is in the picture.
Northam's departure would mean current Lt. Gov. Justin Fairfax, a Democrat who is only the second African-American to win statewide office in Virginia, would be the next governor.
In a tweet, Mr Biden said Mr Northam should resign immediately. We've got a president who wants to divide us.
Indeed, even if Northam had actually expressed hostility to blacks back then, I don't think that says much about him today.
The press conference was filled with multiple embarrassing moments, including one moment when a reporter asked Northam if he could still moonwalk.
The photo was included on Northam's 1984 yearbook page from Eastern Virginia Medical School and was made public on Friday. "As long as I feel that I can lead, I will continue to do that", he said.
The yearbook images were first published on Friday by the conservative news outlet Big League Politics.
The governor's race that Northam won was fraught with racial animosity, with Republican candidates courting Donald Trump's voting base through hardline immigration stances. "The first step is to offer my sincerest apology and to state my absolute commitment to living up to the expectations Virginians set for me when they elected me to be their Governor". This photo makes light of one of the darkest times in our nation's history and is offensive to the millions of people who were tortured, brutalized, and held against their will for hundreds of years.
Tran said she and her family have received death threats through telephone messages, email and social media, leading to extra police protection for her and her family and hard discussions with her young children.
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