North Carolina Lt. Gov. Mark Robinson, the state’s Republican candidate for governor, said he would stay in the race and denied new accusations that he posted racist, antigay and inflammatory comments on a pornography-website message board more than a decade ago.

Trump has yet to speak out as Robinson faces pressures to exit the North Carolina gubernatorial race after reports of his past messages to an adult website.

Mr. Robinson, the Republican nominee for governor of North Carolina, vowed to stay in the race and sought to deny the report, which also said he had defended slavery in online posts years ago.