House Republicans have voted to extend a bill that would ban all abortions after 20 weeks in the District of Columbia to apply in every state in the nation.

The bill would limit a woman's access to abortion even if they learn the pregnancy poses a threat to their health, but it includes an exception in cases where the mother's life is at risk.

The four Democrats on the constitution and civil justice subcommittee voted against the bill, arguing that it was unconstitutional. Campaigners on reproductive rights described the decision by a subcommittee on the constitution to pass such a bill as "astonishing". The bill allows no exceptions for victims of rape or incest.

Trent Franks, a Republican representative from Arizona, introduced his original bill last month to ban such procedures only in the District of Columbia. HR1797, or the DC Pain Capable Unborn Protection Act, is based on the disputed claim that a foetus 20 weeks or older can feel pain.

But following the notorious trial of Kermit Gosnell – a Philadelphia doctor who performed abortions well beyond the legal limit and was convicted of killing three babies after they born alive – Franks amended the bill so it would apply nationwide.

In a statement released on his website on Tuesday, Franks said: "I understand the unfortunate reality that today's markup will be surrounded by some degree of controversy. But we, as a nation, find ourselves at a point at which we don't offer unborn children even the most basic protections – even protections we extend to animals and property. The trial of Kermit Gosnell exposed late abortions for what they really are: relocated infanticide."

He added: "I pray we use this as a 'teachable moment,' in the words of President Obama, and can agree that, at the very least, we are better than dismembering babies who can feel every excruciating moment. I look forward to the bill's moving on the full judiciary committee and to an eventual vote on this necessary, common-sense measure."

Nancy Northup, president and CEO of the Center for Reproductive Rights urged the full House judiciary committee members to reject the bill. She said: "This assault on the health, dignity, and rights of women was dangerous and unconstitutional when it was aimed at the women of Washington, DC, and has only become more reprehensible now that it has been amended to apply to all women across the US."

It is, she said, "every woman's constitutional right to make her own medical decisions without interference from politicians who presume to know better."

"It is astonishing that the subcommittee on the constitution would support such a clear affront to the US constitution – especially when everywhere similar laws have been challenged in the courts, they have been immediately blocked."

Last month, a similar ban on abortions after 20 weeks in Arizona was struck down by the ninth circuit court of appeals. Earlier this year, a similar law in Idaho was ruled unconstitutional by a federal district judge, and a state court temporarily blocked a 20-week ban in Georgia in December 2012.

Cecile Richards, president of Planned Parenthood of America, said: "This outrageous attack on women and their access to safe and legal abortion will not stand. Speaker Boehner should stand by his commitment to focusing on the issues important to the American people by refusing to bring this unconstitutional and deeply dangerous legislation to the floor.

"While abortions later in pregnancy are uncommon, it is important that a woman and her doctor have every medical option available to protect her health. We must have and enforce laws that protect access to safe and legal abortion, and we must reject misguided proposals like this one that would limit women's health care options."

The 1973 Roe v Wade US supreme court ruling established that the constitution protects a woman's right to terminate a pregnancy in cases where a foetus would not survive outside the mother's body, usually judged at 24 weeks.