Story highlights Clinton was invited to appear before the committee investigating the Sept. 11, 2012 terrorist attack earlier this week

Clinton's supporters argue that the House committee is trying to embarrass the former secretary of state as she runs for president

Boston (CNN) Hillary Clinton's campaign said Saturday morning that she will publicly testify before the House Select Committee on Benghazi on Oct. 22. But a committee spokesman later said the former secretary of state's lawyer was demanding limitations on the questioning, casting doubt over whether she'll appear.

Clinton was invited to appear before the committee investigating the Sept. 11, 2012 terrorist attack earlier this week, and the former secretary of state and 2016 presidential candidate accepted that invitation on Friday, campaign spokesman Nick Merrill said.

Merrill said Clinton was "pleased" to receive the invitation to a public hearing from committee chairman Rep. Trey Gowdy. A Democratic Benghazi Commitee spokesperson told CNN that Gowdy offered several dates in October.

But Jamal Ware, the select committee's communications director, disputed that a date had been set, saying that Clinton's lawyer, David Kendall, was insisting that the scope of the questioning be limited to the Benghazi attack -- and not other subjects, such as Libya and her use of a private email server, as Ware claims Kendall had previously agreed to -- and that the hearing date would not change.

"The committee will not, now or ever, accept artificial limitations on its congressionally-directed jurisdiction or efforts to meet the responsibilities assigned to the committee by the House of Representatives," Ware said in a statement. "Accordingly, once there is an agreement on the date and a better understanding of how, if at all, Secretary Clinton's lawyer's latest writing differs from previous ones, the committee will announce said hearing date."

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