It would also drop the current test for an abortion after 20 weeks, which can be approved if deemed necessary to save the woman's life or prevent serious injury.
The bill would mean there would be no legal test for earlier than 20 weeks, leaving the decision up to the woman and her doctor.
For later than 20 weeks, a medical practioner would have to agree that an abortion is appropriate, having regard to the woman's physical and mental health and wellbeing.
The committee said that standard medical practice would see a doctor "always consult colleagues before performing abortions after 20 weeks gestation, and they would only be performed if the doctor deemed them medically appropriate".
But that extra consultation was not explicitly written into the original bill, so the committee has recommended adding it.
"The qualified health practitioner would need to consult at least one other qualified health practitioner when considering whether the abortion was clinically appropriate.
"They would need to have regard to all relevant legal, professional, and ethical standards to which they are subject, and the gestational age of the foetus."
The doctor would still need to have regard to the woman's physical and mental health, as well as her wellbeing.
"However, we recommend that the term 'well-being' be extended to 'overall well-being'. This would reflect that well-being can encompass more than just physical and mental health," the committee report said.
The bill retains the 150-metre safe zones around clinics to keep people from being harassed, though committee members David Seymour, from Act, and Agnes Lohan, from National, objected to having a safe area at all.
Seymour said that a safe zone might be needed if we lived in the US, where demonstrations outside a clinic might be more likely.
"Safe zones, as proposed, impair the right to free speech," Seymour said.
"However this legislation is long overdue and is a move in the right direction after over 30 years of parliamentary inaction."
The committee noted the lengthy delays that currently occur for women seeking an abortion - an average wait of 25 days between the first appointment with the referring doctor and having the procedure.
The longer it takes, the safer and less painful it is, according to a report by the Abortion Supervisory Committee.
"We also heard that access to abortion services throughout New Zealand is inequitable, resulting in some women having to travel significant distances for services," the committee report said.
The committee recommended that the Director-General of Health report to the Health Minister at least every five years about whether access to services is timely and equitable.
It also recommended adding that conscientious objections - which would allow medical staff to refuse a service for religious grounds, for example, but have to inform the woman about an alternative service - should not apply in medical emergencies.
Nor should anyone be charged for a service where a conscientious objection is raised, the committee recommended.
The committee received 25,776 written submissions from interested groups and individuals, 92 per cent of which opposed the bill.
The bill will now return to the House for a second reading, probably in March, when a conscience vote will be held.
