Ohio Gov. John Kasich skipped the Nevada caucuses Tuesday, taking a detour to several states voting next month as his campaign pursues a rapidly narrowing path to the Republican presidential nomination.

As he scored a fifth-place finish in South Carolina’s Republican primary Saturday, Mr. Kasich held town hall meetings in Vermont and Massachusetts, which vote in the Super Tuesday contests next week.

Afterward, he didn’t follow his rivals westward to Nevada but headed to campaign stops in two more Super Tuesday states: Virginia and Georgia. He planned to campaign Wednesday in Louisiana and Mississippi, which vote March 5 and March 8, respectively.

His focus on these races is part of a strategy to squeak through Super Tuesday and get to Michigan, Illinois and his home state of Ohio, industrial Midwestern states where he hopes to surge and win big delegate tallies.

The last of the current and former governors in the race, since former Florida Gov. Jeb Bush dropped out Saturday after an embarrassing fourth-place finish in South Carolina, Mr. Kasich now must compete with Sen. Marco Rubio of Florida to become the mainstream alternative to front-runner Donald Trump.

The Republican establishment is quickly coalescing around Mr. Rubio.

What’s more, Mr. Kasich’s plan to cherry-pick states in which to compete likely will leave him far behind in the delegate race, even if he emerges victorious in the winner-take-all contest in Ohio.

“He has no path to nomination,” said Republican strategist Ryan Williams. “He should put his zombie campaign out of its misery and call it a day.”

The Kasich campaign said the primary calendar was setting up a “tight race” between the governor and Mr. Rubio, citing polls that showed them in competition for third place in Vermont, Massachusetts, Michigan and North Carolina.

The campaign also pointed to polls that showed Mr. Kasich as the only candidate beating Democratic front-runner Hillary Clinton in theoretical matchups, according to a polling average by The Huffington Post.

Mr. Kasich’s campaign got a shot in the arm when he came in second in the New Hampshire primary behind Mr. Trump and ahead of Sen. Ted Cruz of Texas, who is vying for the role of conservative alternative to front-running real estate mogul and reality TV star.

But Mr. Kasich failed to capitalize on the momentum heading into South Carolina.

His run since New Hampshire has been a series of missteps and awkward moments on the stump.

He stumbled again Monday in Virginia, offending women when he said his start in politics more than three decades ago was fueled by “women who left their kitchens” to campaign for him.

“How did I get elected? I didn’t have anybody for me,” he said at a town hall meeting in Fairfax, Virginia. “We just got an army of people and many women who left their kitchens to go out and go door to door and to put yard signs up for me.”

“Now you call homes and everybody’s out working. But at that time — early days — it was an army of the women that really helped me get elected to the state Senate,” said Mr. Kasich, who first ran for Ohio Senate in 1978.

A woman in the audience took issue with the kitchen remark.

“First off, I want to say, your comment earlier about the women came out of the kitchen to support you. I’ll come to support you, but I won’t be coming out of the kitchen,” she said.

Mr. Kasich responded: “I gotcha.”

He finished a distant fourth place in a Gravis poll of likely Republican caucusgoers in Nevada, behind Mr. Trump at 39 percent, Mr. Cruz at 23 percent and Mr. Rubio at 19 percent.

The only candidate still in the race whom Mr. Kasich defeated was retired neurosurgeon Ben Carson at 5 percent.

But Mr. Kasich did not do much better in the Super Tuesday states he is targeting.

He placed fourth in Massachusetts, behind Mr. Trump at 50 percent, Mr. Rubio at 17 percent and Mr. Cruz at 10 percent, according to an Emerson College poll released Monday.

Mr. Carson finished last in the survey with 2 percent.

Mr. Kasich also finished fourth in Virginia with 7 percent, trailing Mr. Trump, Mr. Rubio and Mr. Cruz, according to a Christopher Newport University poll.

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