Democratic gubernatorial hopeful Terry McAuliffe agreed Thursday to debate Republican rival Ken Cuccinelli II in a forum that will allow the candidates to directly ask each other questions.

McAuliffe’s campaign dropped objections to the Virginia Bar Association’s debate format, which allows some candidate-to-candidate questions. The VBA, which will host the debate July 20 at the Homestead resort in Hot Springs, Va., has used that format for the past 10 years, said VBA communications coordinator Marilyn Shaw.

McAuliffe’s campaign had objected to the direct questions for reasons that McAuliffe himself declined to explain at an appearance in Richmond this week. The former Democratic National Committee chairman said that he was not personally involved in the “silly” debate over debate rules, contending that his staff was handling it.

McAuliffe agreed months ago to five debates. Cuccinelli, Virginia’s attorney general, has challenged McAuliffe to 15 across the state. They are running to succeed term-limited Gov. Robert F. McDonnell (R).

As it announced that it had dropped its objections to the VBA debate format, McAuliffe’s campaign said it had done so only because Cuccinelli’s campaign had threatened to pull out of the debate — an account Cuccinelli’s camp disputed.

“The agreement includes candidate-to-candidate questions, after Ken Cuccinelli’s staff refused to discuss compromises proposed by the VBA and threatened to walk away,” a statement from McAuliffe’s campaign said.

Cuccinelli campaign strategist Chris LaCivita said that was not true.

“I was the one in the room,” LaCivita said. “At no time did either campaign — Cuccinelli or McAuliffe — threaten to walk away. Why would we walk away from a debate when we want 14 more?”

Shaw declined to comment on the McAuliffe campaign’s claim about a threatened Cuccinelli withdrawal, noting that the association is a nonpartisan outfit.

But she did say this much: “I think our discussions were very professional.”