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“Sure we may fail. And you want to dump it on me? I may fail. I don’t care. It’s worth doing. It’s worth the effort. And the United States has a responsibility to lead, not always to find the pessimism and negativity that’s so easily prevalent in the world today,” Mr. Kerry said.

While Mr. McCain has made regular practice of criticizing the Obama administration’s foreign policy during recent months, Tuesday’s exchange suggested the senator’s frustration toward Mr. Kerry in particular has reached new heights.

If nothing else, it signals a departure from past years during which the men took care to keep their political differences out of the spotlight, and even kept up appearances of being genuine friends.

Both Vietnam veterans, the two formed an alliance across party lines on repeated occasions during the early 1990s, working closely together on an investigation into missing U.S. prisoners of war and on initiatives to normalize U.S.-Vietnam relations.

When Mr. Kerry was running for president in 2004, he even reportedly pursued Mr. McCain as a potential vice presidential nominee.

While there were lingering ideological differences between the two, their political friendship appeared to reach new heights at a January 2013 Senate hearing on Mr. Kerry’s nomination to replace Hillary Rodham Clinton as the Obama administration’s secretary of state.

“I commend his nomination to you without reservation,” senators were told by Mr. McCain, who appeared at the hearing’s opening beside Mrs. Clinton and freshman Sen. Elizabeth Warren, Massachusetts Democrat, to formally introduce Mr. Kerry.

“He and I have been friends for quite a long time now,” said Mr. McCain, who added that while he and Mr. Kerry have had “political differences” over the years, their friendship is “based in mutual respect.”