NASHVILLE—Sen. Ted Cruz of Texas, who is rising to the top tier of the Republican presidential primary field in Iowa, is plotting a protracted nomination fight through Southern states that are playing bigger roles than in prior elections.

It is a region where his antigovernment, evangelical conservative message plays well, and he has quietly been building a far-reaching political organization to take advantage of that.

If it works, Mr. Cruz could become one of the biggest beneficiaries of the party’s decision to hold primaries in 12 states — half in the South — on March 1. A strong showing by one candidate could provide a burst of momentum at a key moment in the race.

Tennessee is one of the South’s three biggest prizes. As early as August, Mr. Cruz was there touring the state and drawing big crowds. He has dispatched his father Rafael Cruz, a well-known evangelical pastor, to campaign for him multiple times. He has courted legislative endorsements and recruited pastors.

It is a playbook he has used effectively in Iowa, where two polls show him gaining momentum. A Monmouth University Poll of likely GOP caucusgoers released this week showed Mr. Cruz at the top of the field after a steep collapse in support from evangelical Christian voters for retired neurosurgeon Ben Carson. A separate CNN poll showed him moving into second place in the state behind businessman Donald Trump.

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