(CNN) Democratic states are seeking to block new Trump administration rules that would make it harder for some women to get birth control at no cost.

Lawyers for California and Pennsylvania appeared in separate district courts this week to challenge the rules, which would allow more employers to get exemptions to the Affordable Care Act's mandate requiring them to provide insurance coverage for contraceptives with no co-pay.

The rules are scheduled to take effect on January 14.

The first one would allow non-profit and for-profit employers, including publicly traded companies, to receive an exemption based on their religious beliefs. The second would let all but public companies obtain an exemption based on moral objections. Government employers cannot request exemptions.

The changes are part of the Trump administration's efforts ton roll back regulations that conflict with some Americans' religious beliefs. The alterations to the contraceptive mandate's exemptions were first unveiled in the fall of 2017, and final rules were issued in November.

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