Catholic bishops in Virginia are deeply disappointed with Gov. Terry McAuliffe for vetoing the religious freedom bill, saying that because of this faith-based groups that support traditional marriage will no longer have protections.

"The Virginia Catholic Conference is deeply dismayed by the governor's action," the group said. "This veto risks the destruction of Virginia's long tradition of upholding the religious freedom of faith communities which dates back to Thomas Jefferson."

Senate Bill 41 would have prevented the state from punishing religious groups that adhere to their religious belief that marriage is between a man and a woman, the Catholic News Agency reported.

Bishops said the bill would ensure "that clergy and religious organisations are not penalised by the government."

McAuliffe, a Democrat, vetoed the bill saying that the measure would be "making Virginia unwelcomed to same-sex couples, while artificially engendering a sense of fear and persecution among our religious communities."

He said corporate leaders warned that the bill is bad for business.

"They don't want headaches coming from the state," he said.

The governor said the bill will make same-sex couples unwelcome in Virginia.

But the bishops said the measure does not apply to businesses as it only "simply affirms the right of religious organisations to follow their religious beliefs."

They said that with his veto, McAuliffe "marginalises religious believers who hold to the timeless truth about marriage."

"Marriage is the first institution, written in natural law and existing before any government or religion, and is between one man and one woman," the conference said. "Recognising and honouring this institution is not discrimination, but counting people's faith against them most certainly is."

Bill sponsor Republican state Sen. Charles Carrico Sr. told the Washington Post that lawsuits can now be filed against churches in the U.S., noting that the trend now is to promote homosexual beliefs.

There are proposals to override the veto but it is very unlikely, according to the Associated Press.

In Georgia, Republican Gov. Nathan Deal also vetoed a similar religious freedom protection bill.