If Mr. Northam does ultimately resign, Lt. Gov. Justin Fairfax, who is black, would become the state’s governor. Mr. Fairfax broke his silence after the governor’s news conference, but did not directly urge him to stay or go, saying in a statement that “we must make decisions in the best interests of the people of the Commonwealth of Virginia.”

The governor said he had spoken with Mr. Fairfax, 39, several times since the yearbook photo first emerged. “I plan to continue to lead,” Mr. Northam said, before slightly opening the possibility that he could quit. “If we get to the point that we feel we are not effective, we are not efficient,” he said, he would “revisit this.”

That possibility grew far more likely shortly before 7 p.m. Eastern time, when Mr. Warner, Mr. Kaine and Mr. Scott, an African-American who is the dean of the state’s congressional delegation, issued their statement.

“Governor Northam has served the people of the Commonwealth faithfully for many years, but the events of the past 24 hours have inflicted immense pain and irrevocably broken the trust Virginians must have in their leaders,” said the three lawmakers, who initially resisted calling on the governor to quit. “He should step down and allow the Commonwealth to begin healing.”

Mr. Northam, standing next to his wife, Pam, at the news conference, spoke earnestly and was seemingly impervious to the wave of condemnation that the photograph had spawned. He appeared determined to maintain his innocence, and said he would use the controversy as something of a teachable moment in the state where slaves first arrived 400 years ago.

Speaking to reporters for over 40 minutes as a handful of protesters gathered outside the State Capitol demanding that he resign, the 59-year-old governor said he wanted to have “an honest conversation about racial justice.”

Mr. Northam called the image of the two men “offensive, racist and despicable.” But he said, “I cannot in good conscience choose the path that would be easier, for me to duck my responsibility to reconcile.”