The move is an attempt to override President Obama, who has offered a compromise that would shift the cost of covering contraception from religious organizations (such as universities and hospitals) to insurance companies. Republicans have rejected that compromise as insufficient.

“This is an extreme attack on every one of us,” Warren told the newspaper. “It opens the door to outright discrimination. It would let insurance companies and corporations cut off pregnant women, overweight guys, older Americans, or anyone, because some executive claims it’s part of his moral code."

Brown's campaign reacted by calling it elitist to dictate how religious people should act or behave, and said that by supporting a religious conscience exemption, Brown was following in the footsteps of former Sen. Edward Kennedy (D-Mass.).

"She wants to use the power of government to force Catholics to violate the teachings of their faith. That is wrong," Brown said in a statement.

Warren and Brown are fighting for the seat Brown won in a 2010 special election to replace Kennedy, who held the seat for more than four decades until he died while in office.

Earlier Tuesday, a WBUR poll showed Warren with 46 percent compared to Brown's 43 percent — within the margin of error.

This post was updated at 7:39 p.m.

Listen to Brown's ad: