Arizona Gov. Doug Ducey has appointed former Republican Sen. Jon Kyl to fill the Senate seat vacated by the passing of Sen. John McCain. Ducey formally announced his selection in a news conference in Arizona Tuesday.

Ducey said, "we're all aware of the size of the void John McCain leaves," and there is "no replacing" McCain. But the law requires him to select someone who can serve the people of Arizona, and Ducey said he sees no one better suited to do so. Kyl served from 1995 to 2013 in the U.S. Senate, where he worked alongside McCain.

"There is no one in Arizona with the stature of Senator Jon Kyl," Ducey said Tuesday. "He's a man without comparable peer."

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It's unclear how long Kyl will serve in the Senate. Ducey said he hasn't received an assurance from Kyl that he will serve through 2020, but Kyl has agreed to serve at least through the current term in Congress, "and it's my hope that he serves longer." Legally, the appointment could last through 2020, when there is expected to be a special election for the two remaining years in McCain's term. Kyl said he doesn't intend to run for the seat in the future, or for any other seat.

Kyl has expressed concerns with the president's temperament in the past, saying at one point saying Mr. Trump is his "own worst enemy." Kyl said he stands by his prior comments.

"I think sometimes his desire to jump into the middle of the fight ... Sometimes that can be detrimental to what he's trying to achieve," Kyl said Tuesday.

Many speculated that Ducey might pick a McCain family member — either his wife, Cindy, or daughter Meghan — to fill the seat. Cindy McCain expressed her support for Kyl in a tweet ahead of Ducey's announcement.

"John Kyl [SIC] is a dear friend of mine and John's. It's a great tribute to John that he is prepared to go back into public service to help the state of Arizona," she tweeted.

Meghan McCain, too, praised the choice.

"I'm very grateful to Jon Kyl for his willingness to return to public service to take my father's seat in the Senate," she tweeted. "I can think of no one better to keep fighting for the country and state he held so dear. He has always been a true statesman and a friend to my family."

Retiring Sen. Jeff Flake, R-Arizona, who succeeded Kyl, said there is "no one more qualified."

"Jon Kyl is an excellent choice to fill John McCain's Senate seat. There is no one more qualified. Arizona will be well-served by Jon's willingness to once again serve his country," Flake said.

Ky has been one of the "sherpas" escorting Supreme Court nominee Brett Kavanaugh through the Senate confirmation process. He also spoke at the brief ceremony at the Arizona Capitol last week before the public was invited in to see McCain lying in state.

— CBS News' Christina Ruffini, Ed O'Keefe, Kathryn Watson and Nancy Cordes contributed to this report