Rienzi said the ruling could have far-reaching consequences.
He said that the Obama administration has consistently held a "stingy view" of what qualifies as religion under the law.
This view is exemplified in the very narrow religious exemption permitted by the Health and Human Services mandate requiring health insurance providers to cover contraception, he said.
By unanimously upholding the rights of religious groups, the court has struck a "very big blow" to the administration's narrow definition of religion, which it described as "extreme," "remarkable" and "untenable," Rienzi said.
He explained that the decision could have "ripple effects" as courts continue to examine the contraception mandate and other decisions by the Obama administration dealing with the freedom of religious organizations.
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Bishop William E. Lori of Bridgeport, chairman of the U.S. bishops' ad hoc Committee on Religious Liberty, hailed the court's decision as "a victory for religious liberty and the U.S. Constitution."
"Freedom of Religion is America's First Freedom and the Court has spoken unanimously in favor of it," he said. "The Founding Fathers would be proud."
Bishop Lori said that the ruling "makes resoundingly clear the historical and constitutional importance of keeping internal church affairs off limits to the government."
He observed that the ability of churches to choose their ministers is important because "whoever chooses the minister chooses the message."
"It is a great day for the First Amendment," he said.
Michelle La Rosa is deputy editor-in-chief of Catholic News Agency. She has worked for CNA since 2011. She studied political philosophy and journalism at the University of Dallas.