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BOSTON — Bracing for a finish toward the bottom of the pack in South Carolina, the campaign of Gov. John R. Kasich of Ohio argued on Saturday that the primary’s outcome would be a victory no matter what because of Jeb Bush’s struggles.

Mr. Kasich’s chief strategist, John Weaver, said the race would be down to four viable candidates after Saturday’s primary: Donald J. Trump, Senator Ted Cruz of Texas, Senator Marco Rubio of Florida and Mr. Kasich.

“For all practical purposes, there’s no path forward for Governor Bush,” Mr. Weaver said on a conference call with reporters.

Referring to Saturday’s outcome in South Carolina, he said, “We’ve already won there, at least in my sense, because however we do, it’s going to help drive somebody else out of the race” — with that somebody being Mr. Bush.

Tim Miller, a spokesman for Mr. Bush, responded by saying that Mr. Kasich was “running a zombie campaign that exists only in three states in the hopes that he can gain some cachet in the vice-presidential sweepstakes.”

“They do not even pretend to have a plan to earn the delegates needed to win the nomination,” he said. “This is just a classless attempt to impact the Election Day vote in a state that John Kasich cut and run from a few days ago. We look forward to beating him here in South Carolina and moving on to Nevada, another state John Kasich has given up on.”

On Friday, his last day of campaigning in South Carolina, Mr. Kasich also tried to frame his effort in South Carolina as a success, saying that he had been expected to receive “maybe two or three votes,” a bar he said he would clear.

Mr. Kasich is now focusing on more hospitable states that have primaries in the next few weeks.

Earlier this week, he visited Michigan, which votes March 8. And instead of sticking around in South Carolina for Saturday’s primary, he campaigned in New England, holding town-hall-style forums in Colchester, Vt., and Worcester, Mass. Both Vermont and Massachusetts have their primaries on March 1.