US politicians have voted to restore abortion rights nationwide in the first legislative response to the Supreme Court's landmark decision overturning Roe v Wade.

The bill has little chance of becoming law, with the necessary support lacking in the 50-50 Senate.

Yet voting marks the beginning of a new era in the debate as politicians, governors and legislatures grapple with the impact of the court's decision.

The legislation passed 219-210.

The House also passed a second bill to prohibit punishment for a woman or child who decides to travel to another state to get an abortion, by 223-205.

"Just three weeks ago the Supreme Court took a wrecking ball to the fundamental rights by overturning Roe v Wade," House Speaker Nancy Pelosi said ahead of the votes.

"It is outrageous that 50 years later, women must again fight for our most basic rights against an extremist court."

Republicans spoke forcefully against the two bills, praising the Supreme Court's decision and warning the legislation would go further than Roe ever did when it comes to legalising abortion.

Urging her colleagues to vote no, Washington Republican Cathy McMorris Rodgers called abortion "the greatest human rights issue of our generation".

She said the Democratic legislation "has nothing to do with protecting the health of women. It has everything to do with forcing an extreme agenda on the American people".

The White House hailed Friday's votes as an "important step".

"These bills would ensure women's access to essential healthcare services, regardless of where they live, and protect the bedrock right to cross state lines for medical care," White House press secretary Karine Jean-Pierre said.

"A majority of Americans across the country support them."

By overturning Roe, the court has allowed states to enact strict abortion limits, including many that had previously been deemed unconstitutional.

A number of Republican-controlled states have moved quickly to curtail or outlaw abortion, while states controlled by Democrats have sought to champion access.

Voters now rank abortion as among the most pressing issues facing the country, a shift in priorities Democrats hope will reshape the political landscape in their favour for November's midterm elections.

This is the second time the House has passed the bill, which would expand on the protections Roe had previously provided by banning what supporters say are medically unnecessary restrictions that block access to safe and accessible abortions.

It would prevent abortion bans earlier than 24 weeks, which is when fetal viability - the ability of a human fetus to survive outside the uterus - is generally thought to begin.

It allows exceptions for abortions after fetal viability when a provider determines the life or health of the mother is at risk.

The bill that would prohibit punishment for travelling out of state would specify that doctors cannot be punished for providing reproductive care outside their home state.

Democrats have highlighted the case of a 10-year-old girl who had to cross state lines into Indiana to get an abortion after being raped, calling it an example of how the court's decision is already having severe consequences.

"We don't have to imagine why this might matter. We don't need to conjure up hypotheticals. We already know what's happened," Democratic Senator Amy Klobuchar said on Thursday.

Democrats have teed up more bills for passage in the coming weeks. Majority Leader Steny Hoyer said on Friday that the House will vote next week on legislation guaranteeing a right to contraception.

Republican Senator James Lankford of Oklahoma, who supports instituting a nationwide ban on abortion, accused Democrats of seeking to "inflame" the issue of abortion.

He said proponents of the travel bill should ask themselves, "Does the child in the womb have the right to travel in their future?".

President Joe Biden, who denounced the court's ruling as "extreme", last week issued an executive order intended to head off some potential penalties that women seeking abortion may face.

His administration also warned medical providers they must offer abortion if the life of the mother is at risk.