Pro-choice groups are moving to have an entire section in the Criminal Code revoked in the hope of giving women with unwanted pregnancies the right to legal abortion and protect medical personnel performing the procedures from facing legal action.
The Choices Network Thailand (CNT), however, insisted it was not advocating "free abortions".
CNT coordinator Krittaya Atchawanitchakun said the network and other organisations have sought to make the changes to the Criminal Code governing abortion.
The groups petitioned Mukda Phongsombat, chair of the House standing committee on society, children, youth, women, the elderly, the disabled and the underprivileged.
More than 40 civil organisations and 1,500 individuals have signed the petition in support of the move to revise the code.
"We want no more deaths or injuries from abortions," Ms Krittaya said. "Abortions must be safe to practise, but it does not mean we want free abortions."
She said Section 301 stipulates that women can face imprisonment for up to three years or be fined up to 60,000 baht for carrying out an abortion or having someone else perform the procedure.
The groups want this section scrapped, saying women are being unfairly blamed for getting pregnant.
Under Section 302, a person who aborts a pregnancy, even with the consent of the pregnant woman, could be jailed for up to five years and fined 100,000 baht.
It also says that if an abortion procedure causes a woman to be critically injured, the offender could be jailed for up to seven years and fined 100,000.
In the case of an abortion procedure that causes a woman to die, the offender could be jailed for up to 10 years and fined up to 200,000 baht.
Under Section 303, whoever causes a pregnancy to be aborted without the consent of the woman can face a prison term of up to seven years and a fine of 140,000 baht.
If the abortion results in the woman being critically injured, the offender faces a jail term of between one and 10 years and a fine between 20,000 and 200,000 baht.
If an abortion causes a woman to die, the offender may be jailed for between five and 20 years and be fined between 100,000 and 400,000 baht.
Under Section 304, anyone attempting to commit offences mentioned under Sections 302 and 303 is deemed a criminal.
Ms Krittaya said the groups are pushing to have Section 305 in the Criminal Code amended. Section 305 refers to Section 302.
The groups want the section to be retained but with an added clause to permit consented abortions to be performed by trained medical professionals.
The section says that if a pregnancy is more than 24 weeks old, the grounds for an abortion must be broadened. The section allows abortions to be conducted if mothers suffer physical or mental health issues or have been raped.
The groups also called for other issues to be recognised by law as grounds for abortion, saying women should be able to end pregnancies caused by failed contraception or if she experiences economic hardship and is unable to provide sufficient care to the child.
Women should also be legally allowed to abort pregnancies if foetuses display physical disability or develop severe genetic disorders.
"We are working to achieve having fewer deaths and injuries from abortions," Ms Krittaya said.