Gov. Andrew M. Cuomo has not been accused of wrongdoing, and under state law the attorney general lacks the power to investigate him even if he had. But that didn’t stop his fellow Democrats vying to run for attorney general to say on Tuesday that they would be open to doing just that.

All four candidates, including one endorsed by Mr. Cuomo, were asked in a taped debate that airs on Wednesday if they “support calls for an investigation into the governor” for the use of state government offices for campaign purposes by a top Cuomo aide convicted in March on federal corruption charges.

No one said they did not.

“If individuals used a public office for political purposes, they should be prosecuted to the fullest extent of the law. What I, as the next attorney general, will do is follow the evidence and the facts wherever it leads and if it leads to the second floor, so be it,” Letitia James, the city’s public advocate who has the support of Mr. Cuomo as she runs for the Democratic nomination for attorney general, said in reference to the location of the governor’s office at the Capitol.

“Anytime there is corruption at that level of state government, the person at the top of state government should say ‘I’m the accountable person, the buck stops here with me,’” said another candidate, Representative Sean Patrick Maloney. “You shouldn’t be afraid of the truth, you shouldn’t be afraid of a full investigation, and that’s what should happen.”