Mr. Kobach, a former Kansas secretary of state, was the Republican nominee for governor there last year. He lost to Laura Kelly, the Democratic candidate, by five percentage points in a state regarded as reliably Republican. Since that stinging loss, members of the party had expressed concern that Kansas voters were seeking a more moderate platform than the one championed by Mr. Kobach.

Noting that loss, the National Republican Senate Committee, which raises money for Republican Senate candidates, issued a statement indicating that Mr. Kobach would not receive its endorsement.

“Just last year Kris Kobach ran and lost to a Democrat,” said the statement, issued by an N.R.S.C. representative. “Now, he wants to do the same and simultaneously put President Trump’s presidency and Senate Majority at risk. We know Kansans won’t let that happen and we look forward to watching the Republican candidate they do choose win next fall.”

In a telephone interview after his announcement, Mr. Kobach discounted the N.R.S.C. statement, saying: “There are some in the establishment who dislike a candidate who thinks for himself and isn’t easily controlled by the Washington establishment. I will be someone who will be taking a firm stand on principle and will not be knuckling under whenever the establishment snaps its fingers.”

Mr. Kobach said that immigration would be one of three pillars of his campaign, along with cutting government spending and preserving the Constitution.