"It was a complete dereliction of duty," said Rep. Todd Rutherford, D-Columbia, adding that Rep. Bakari Sellers, R-Denmark, had also called for Mr. Sanford to step down. Mr. Rutherford said Mr. Sanford's deceit and unexplained absence trumped his extramarital affair.
"I'm not the 'moral majority,' and I am not going to take my Bible around and beat people on the head with it," he said. "But if his wife didn't care where he was, why couldn't he tell his staff?"
Half of South Carolinians believe Mr. Sanford, 49, should quit, after his admission Wednesday that he had been having an affair with a woman in Argentina, according to an InsiderAdvantage poll commissioned by The Politico Web site.
During his news conference, Mr. Sanford did not respond when asked whether he would resign. If he does, the office would fall to Andre Bauer, the state's lieutenant governor and second highest constitutional officer.
Frank Adams, the communications director for Mr. Bauer's office, declined to comment on whether the office was making any preparations to assume the governor's responsibilities.
South Carolina House Speaker Bobby Harrell criticized the governor for his actions and pointed to the need for new legislation clarifying who is in charge when the governor is gone.
"The governor's absence has brought to light some issues regarding the chain of command in the absence of the chief executive," said the Charleston Republican in a statement. "It is imperative that the General Assembly deal with this during the next session."
Asked Thursday whether Mr. Sanford should resign, Mr. Harrell said through a spokesman, "The governor needs to decide if he can be an effective chief executive for the state of S.C. and make his decision accordingly."
Of prominent Republicans, only Glenn McCall, one of South Carolina's Republican National Committeeman, has publicly called for Mr. Sanford's resignation, according to Greg Foster, spokesman for Mr. Harrell.
"Personally I don't think that it is necessary for him to resign as governor," said state Rep. Kenneth Hodges, D-Green Pond.