In his most audacious attack yet on a revered public figure, Donald J. Trump veered into risky political territory on Thursday as he denounced Pope Francis, seeking to galvanize Republicans who worry about border security and appeal to evangelical voters who regard Francis as too liberal.

After the pontiff’s remarkable contention that Mr. Trump “is not Christian” in proposing deportations and a wall with Mexico, the candidate said Francis’ criticisms were “disgraceful” and “unbelievable,” and he contended that the Mexican government had hoodwinked the pope into criticizing him.

Politicians rarely rebuke the Vatican so forcefully for fear of alienating Catholic voters, but Mr. Trump has been increasingly aggressive ahead of Saturday’s primary in South Carolina, where polls show a tightening race and the popular Republican governor, Nikki R. Haley, just endorsed Senator Marco Rubio of Florida.

Mr. Trump’s attack on Francis reflected a political calculation that criticizing the pope would not hurt him with conservatives and might even improve his standing in South Carolina and in the Southern-dominated Super Tuesday contests on March 1. Some evangelical denominations in the South and elsewhere take a dim view of the Catholic Church, and many other social conservatives have been critical of Francis over his relatively measured statements about gays, birth control and divorce.

Attacking the pope could energize conservatives who think that Mr. Trump will go to greater lengths to halt illegal immigration than establishment politicians and power brokers like the Holy See, according to political strategists in both parties.

Still, the spectacle of the flamboyant billionaire businessman facing down the global leader of 1.2 billion Catholics was the presidential campaign’s most revealing example of Mr. Trump’s emotional instinct to make punching bags of those who cross him, whether it is Senator Ted Cruz of Texas, the leaders of longtime allies like Mexico, or the bishop of Rome.