Donald Trump has rolled back requirements under Obamacare that forced employers to provide insurance to cover women's birth control.

The new rules followed up a campaign pledge that delighted conservative Christian supporters and will allow businesses or charities to lodge religious or moral objections to gain an exemption from the commitment.

Evangelical Christians were particularly pleased with Russell Moore, president of the ethics and religious liberty commission of the Southern Baptist Church, calling the previous law 'an unlawful overreach, forcing a choice between obedience to God and compliance with the regulatory state'.

However women's rights activists and Democrats criticised the move and within hours the American Civil Liberties Union sued Trump's adminstration in a bid to halt the change.

It is unclear how many employers would actually drop birth control coverage on religious grounds, and there were significant doubts that many big ones would.

'This is a landmark day for religious liberty. Under the Obama administration, this constitutional right was seriously eroded,' Republican House of Representatives Speaker Paul Ryan said.

But Planned Parenthood's President Cecile Richards said: 'The Trump administration just took direct aim at birth control coverage for 62 million women.'

Richards added: 'With this rule in place, any employer could decide that their employees no longer have health insurance coverage for birth control.'

Trump, who criticised the birth control mandate in last year's election campaign, won strong support from conservative Christian voters. The Republican president signed an executive order in May asking for rules that would allow faith-based groups to deny insurance coverage for services they oppose on religious grounds.

The contraception mandate was implemented as part of the 2010 Affordable Care Act, Democratic former President Barack Obama's signature achievement. Trump and Republicans in Congress campaigned against Obamacare, as the law is known, but could not get enough votes to repeal it as they had promised.

In its reasoning for the move, the administration said among other things that mandating birth control coverage could foster 'risky sexual behaviour' among teens and young adults. It overturned the Obama administration's view that the birth control requirement was necessary to meet the government's 'compelling interest' to protect women's health.

'This administration's contempt for women reaches a new low with this appalling decision,' top House Democrat Nancy Pelosi said.

The administration broadened narrow existing religious exemptions to include an exception "on the basis of moral conviction" for non-profit and for-profit companies.

Federal rules implemented under Obamacare required employers to provide health insurance that covers birth control, but religious houses of worship were exempted. Some private businesses sued regarding their rights to circumvent such coverage, and the Supreme Court ruled in 2014 that they could object on religious grounds.

Mark Rienzi, one of the lawyers for the Little Sisters of the Poor who were involved in a legal challenge to Obama's rule, said: 'HHS has issued a balanced rule that respects all sides - it keeps the contraceptive mandate in place for most employers and now provides a religious exemption.

The Little Sisters and other Christian nonprofit employers objected to a 2013 compromise offered by the Obama administration that allowed entities opposed to providing contraception insurance coverage to comply with the law without actually paying for the required coverage.

The Justice Department released two memos that will serve as the government's legal basis for justifying the rule and laying out a framework for how apply religious liberty issues in legal opinions, federal rules and grant making.

In another decision popular with Trump's evangelical supporters, the Justice Department on Wednesday reversed federal policy and declared that federal law banning sex discrimination in the workplace does not protect transgender employees. Trump also has removed protections for transgender students and moved to ban transgender people from the military.

Trump's support among evangelical voters, a major force in his 2016 election victory, remains strong, but has been slipping in line with his overall approval ratings, according to recent Reuters/Ipsos poll results.

Additional reporting by Reuters.