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“It’s now moot because [Mr. Assad] has made a set of judgments that are inexcusable, that are reprehensible and, I think, [he] is not long for remaining as the head of state in Syria,” Mr. Kerry said.

He also faced tough questions about the attack last year on the U.S. Consulate in Benghazi, Libya, that killed four Americans, including Ambassador J. Christopher Stevens. The attack raised questions about the department’s security arrangements, and Sen. Ron Johnson, a Wisconsin Republican who on Wednesday pointedly questioned Mrs. Clinton’s handling of the incident, asked Mr. Kerry his thoughts.

“Senator, if you’re trying to get some daylight between me and Secretary Clinton, that’s not going to happen,” Mr. Kerry responded.

Sen. Rand Paul, Kentucky Republican, accused Mr. Kerry of flip-flopping on whether the Constitution prevents a president from authorizing military attacks without congressional approval.

Mr. Kerry supported President Obama’s 2011 deployment of American forces to run a no-fly zone over Libya, though he opposed the tactic decades ago with regard to U.S. bombings of Vietnam and Cambodia.

“Look,” responded Mr. Kerry, “you can be absolutist and apply it to every circumstance. The problem is it just doesn’t work in some instances.”