In an interview Tuesday with a Fayetteville, Ark., radio station, Cotton was asked about the Supreme's Court decision to allow some businesses to opt out of health coverage for contraceptives, citing religious freedoms.
Pryor did not entirely disavow the ruling, saying in a statement, "As a person of faith, I understand the deeply held religious views of those who brought this suit forward."
"At the same time I cannot support Congressman Cotton’s irresponsible plan to return to the days when women paid more than men for basic health care services," Pryor added.
In a statement Wednesday, Pryor's campaign demanded an apology from Cotton, while Pryor expressed disappointment in what he called Cotton's "deeply personal" attack.
“[Cotton] and I may disagree on issues, but for him to question my faith is out of bounds," Pryor said.
But in a statement passed along by a spokesperson, Cotton did not apologize for his remarks.
"Sen. Pryor is a man of faith and practices it with commendable openness, which I respect, but I wish he would respect Arkansans' right to practice our faith," Cotton said. "Instead, Sen. Pryor and President Obama still defend Obamacare even after the Supreme Court said it violated freedom of religion. Sen. Pryor supports taxpayer-funded abortion and late-term abortion and would force Christians to pay for abortions despite their deeply held religious beliefs. That's a real attack on faith."
Pryor has not been outspoken on abortion issues, but he has in general taken votes to limit the practice. In 2003, Pryor supported a ban on partial-birth abortions except when the mother's life is endangered.
The race between Pryor and Cotton, among the most closely watched Senate contests this cycle, could tilt control of the Senate in either party's favor. But Pryor, who Republicans thought to be particularly vulnerable among Democratic incumbents, has so far been holding on to a slight lead in public polls.
Pryor's campaign apparently foresaw religion as an undercurrent issue the race and sought to establish Pryor's credibility early, with a television ad in December that featured Pryor with a copy of the Bible.
"I'm not ashamed to say that I believe in God, and I believe in His word," Pryor said in the ad. "The Bible teaches us no one has all the answers, only God does, and neither political party is always right."
"This is my compass, my North Star," Pryor continued, holding up the Bible. "It gives me comfort and guidance to do what's best for Arkansas."
Former Arkansas Gov. Mike Huckabee, a Republican, did not question Pryor's religious convictions during a December episode of his radio show, saying he had instead concluded from conversations with Pryor that "his faith is very real."
"I don't think that you can judge a person's faith, or the authenticity of it, based on their politics," Huckabee said.
An attack on a Democratic candidate's religious values has backfired before for Republicans. In North Carolina in 2008, Republican Sen. Elizabeth Dole's campaign aired an attack ad accusing Democrat Kay Hagan of accepting money from an anti-religion group, the Godless Americans Political Action Committee. The ad ended with a photo of Hagan over a woman's voice saying, "There is no God."
Hagan lambasted the ad as "an attack on my Christian faith" and filed a defamation lawsuit. Dole ultimately lost her re-election bid to Hagan.