Conservative MP Nadine Dorries has suggested abortion advice in England should not be given by organisations that carry out terminations.
The government says it is committed to making sure counselling is independent.
Some Tory MPs say they are angry at what they see as an attempt to put them under pressure during a Commons debate.
Downing Street earlier made it clear Prime Minister David Cameron opposed Ms Dorries' amendment to the Health and Social Care Bill.
However, a spokesperson said that no pressure was being applied to Conservative MPs to vote in a particular way.
The bill is due to be discussed by MPs in the Commons on Tuesday and Wednesday but it is not yet certain that the amendment will even be heard, says BBC political correspondent Ben Geoghegan.
At present, women seeking an abortion need the consent of two doctors, which can be obtained through an NHS clinic or GP surgery, or at a private provider, such as Marie Stopes or the British Pregnancy Advisory Service (BPAS), affiliated to the NHS.
In both cases, staff have a duty to provide counselling to the women who use them - and under Royal College of Obstetricians and Gynaecologists' guidelines that advice should be impartial, objective and unbiased.
Ms Dorries' amendment - which is also supported by Labour backbencher Frank Field - would remove that duty from Marie Stopes and BPAS.
It says the NHS - specifically GPs - should provide "independent information, advice and counselling services for women requesting termination of pregnancy" - and it defines "independent" as an organisation that does not itself provide abortions.
There are no other stipulations about who those independent bodies could be. Pro-choice campaigners say they could be faith-based groups morally opposed to abortion, who will seek to persuade women that going ahead with one would be a sin.
While MPs are traditionally given a "free vote" on abortion, the Department of Health's letter to MPs says all health ministers are against the idea.
The Department of Health says it is looking to consult over the advice available to women seeking terminations and has not finalised any proposals yet.
It says any requirement to offer independent counselling would be in addition to what is already provided by GPs and clinics, not instead of it, and the government does not propose to strip abortion charities of their ability to provide advice.
For more background on the issue, see this article in the Guardian. The responses by Suzanne Moore and David Steel
Ms Dorries' real views on abortion have been reported at Liberal Conspiracy and some people hav taken to writing to Ms Dorries about their wombs, in the hope that this will satisfy her somewhat unhealthy interest in other people's reproductive apparatus without curtailing women's rights. A masterlist of the letters written thus far can be found here.