It says that NHS abortion services are failing women and the law should be changed to allow easier access to early terminations.
FPA is lobbying for amendments to the 1967 Abortion Act, which the charity claims is outdated and based around a moralistic view of abortion that has no relevance in today's society.
"We need an Abortion Act for the 21st Century," said Caroline Davey, head of policy at FPA. "The situation means women are finding themselves ruled out of suitable, safe methods of early abortion due to delays in the system or inadequate funding."
It wants to abolish the requirement for two doctors to sign off every abortion, and allow GPs and nurses to play a greater role in early abortion services.
"This is an area that is widely under-reported and examined," said Davey.
"We'd like to see early abortion fitting into the range of fertility control services available and have it integrated into mainstream sexual health provision."
To kick off the campaign, the charity has written a report that it presented to a meeting of the All-Party Parliamentary Pro-Choice Group today. The report demands an end to the postcode lottery of funding for terminations and recommends that the NHS pays for at least 90 per cent of abortions.
"Things have moved on," said Davey. "We want to highlight that not only is the current abortion service inadequate, but that there are inequalities in the number of NHS-funded terminations, and in waiting times to get the referral by geographical area."
The charity is calling on Primary Care Trusts to prioritise funding for early abortion services, and to set a target waiting time of 72 hours for abortion from the time a woman first contacts a health professional.