(CNN) Several senior Senate Republicans -- including key members of leadership -- criticized the White House's handling of an impolitic comment made last week by a junior aide about Sen. John McCain "dying" and the administration's refusal to apologize and move on.

"I think an apology is appropriate," Sen. John Cornyn of Texas said firmly.

When asked from who, Cornyn said, "From the person who said that really dumb thing."

Cornyn said he would have preferred the White House already put to rest the story, now five days old, which has pitted Trump officials against one of the most revered members of the Senate who is battling an aggressive form of brain cancer.

Despite his illness, the Arizona Republican has remained a vocal and active critic of Trump's, which may explain why the White House is reluctant to make peace.

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