The Senate plans to vet the amendment on early-stage abortion next week.
The bill, which cleared the House of Representatives on Wednesday, is now in the hands of the Senate and the deadline for passing it is approaching fast.
Senate whip spokesman Kamnoon Sitthisamarn said the chamber was scheduled to meet next Monday and Tuesday, with the abortion amendment bill among urgent pieces of legislation on the agenda.
Mr Kamnoon said the Senate's scrutiny panel would join in the debates through the three readings.
The scrutiny is typically exercised in the second reading but the chamber is hosting a seminar today to discuss details of the bill which are sensitive and require careful consideration.
The amendment earlier breezed through its third and final reading in the House -- 276 MPs voted in favour, just eight against and 54 abstained.
Originally, two bills -- one initiated by the cabinet and the other by the Move Forward Party -- were proposed, but the House decided to forward only the cabinet's bill for further scrutiny.
The bill, which seeks to amend abortion-related sections of the Criminal Code, would make it legal for a woman to have an abortion up until her 12th week; previously, abortion was illegal regardless of the age of the foetus.
According to current MCT guidelines, a pregnancy can be terminated if it poses a threat to the mother's physical and/or emotional health; if the foetus is known to have abnormalities; and/or if the pregnancy is the result of a sexual assault. Mr Kamnoon said having the Senate's scrutiny panel for the three readings, would allow for a thorough vetting of the bill.
Thanikarn Pornpongsaroj, deputy chairwoman of the House committee scrutinising the amendment, said it needed to be enacted urgently to beat the deadline for complying with a Constitutional Court ruling.
The court found Section 301 of the Criminal Code in breach of Section 28 of the constitution that refers specifically to people's rights and freedoms in relation to their bodies.
The Criminal Code must be rectified in line with the charter by Feb 12.