Despite the changes made to address religious concerns on the Obamacare contraceptive mandate last week, several religious groups continue to oppose the signature healthcare law under the administration of US President Barack Obama.

The Becket Fund for Religious Liberty said efforts of the Obama administration to address concerns on the birth-control mandate are not enough to ensure religious groups will not be forced to provide contraception to women.

"Especially after the Supreme Court's recent King v Burwell decision allowed the government to expand its healthcare exchanges, there is no reason at all the government needs religious employers to help it distribute these products," the group said in a statement, according to The Guardian.

Becket Fund's legal counsel Adèle Auxier Keim made the remarks after Health and Human Services department officials announced that they have already rewritten the rules for employers who morally object to covering birth control pills in their healthcare insurance plans.

HHS Secretary Sylvia Burwell said the changes were made to respect beliefs and other similar views that are against the Affordable Care Act, particularly its contraceptive mandate that requires employers to cover 20 FDA-approved drugs and services including birth-control or abortion pills at no cost.

Burwell explained the changes to the healthcare law will make it easier for religious organisations not to cover birth control for women.

"Women across the country should have access to preventive services, including contraception. At the same time, we recognise the deeply held views on these issues, and we are committed to securing women's access to important preventive services at no additional cost under the Affordable Care Act, while respecting religious beliefs," Burwell said, according to the Washington Times.

But Americans United for Separation of Church and State does not think Burwell's announcement can temper religious challenges to the contraception mandate.

The group's executive director, the Reverend Barry W. Lynn, blamed the Supreme Court for making such challenges possible with its Hobby Lobby ruling.

"The administration had to respond to this ruling, and today's regulations are a good-faith effort to protect women," Lynn said in an official statement, according to the Guardian.

Even some pro-abortion groups expressed opposition to the new rules, arguing that they give too much "power over the healthcare decisions of the women they employ."

Washington Sen. Patty Murray, a Democrat, argued that the regulations demonstrate why "the Supreme Court's deeply harmful ruling in Burwell v. Hobby Lobby is completely unacceptable."

This concern, the Washington Post reported, prompted Murray to introduce a new bill in Congress, which would override the US Supreme Court decision.