WASHINGTON — The massacre of nine African-Americans in a storied Charleston church last week, which thrust the issues of race relations and gun rights into the center of the 2016 presidential campaign, has now added another familiar, divisive question to the emerging contest for the Republican nomination: what to do with the Confederate battle flag that flies on the grounds of the South Carolina Capitol.

And like some of their predecessors seeking to win the state’s primary, the first in the South, the leading Republican candidates for 2016 are treading delicately. They do not want to risk offending the conservative white voters who venerate the most recognizable emblem of the Confederacy and who say it is a symbol of their heritage.

Jeb Bush issued a statement on Saturday saying he was confident that South Carolina “will do the right thing.” As Florida’s governor, Mr. Bush in 2001 ordered the Confederate flag to be taken from its display outside his state’s Capitol “to a museum where it belonged.”

Senator Marco Rubio, also of Florida, told reporters that he thought the state would “make the right choice for the people of South Carolina.”