WASHINGTON — In his first term, President Obama presided over an administration known for its lack of open dissension on critical foreign policy issues.

But on Thursday, deep divisions over what to do about one of those issues — the rising violence in Syria — spilled into public view for the first time in a blunt exchange between Senator John McCain, Republican of Arizona, and the leaders of the Pentagon.

Testifying before the Senate Armed Services Committee, Defense Secretary Leon E. Panetta acknowledged that he and the chairman of the Joint Chiefs of Staff, Gen. Martin E. Dempsey, had supported a plan last year to arm carefully vetted Syrian rebels. But it was ultimately vetoed by the White House, Mr. Panetta said, although it was developed by David H. Petraeus, the C.I.A. director at the time, and backed by Hillary Rodham Clinton, then the secretary of state.

“How many more have to die before you recommend military action?” Mr. McCain asked Mr. Panetta on Thursday, noting that an estimated 60,000 Syrians had been killed in the fighting.