The Computer Crime Act (CCA) still includes too broad a definition of offences which could lead to abuse by authorities, critics say.
The National Legislative Assembly has postponed the second reading of the bill until next month, but critics say time is running out for the changes they want.
Among their concerns are the bill would allow self-censorship by internet service providers (ISPs) and witchhunts by authorities.
Sam Zarifi, International Commission of Jurists regional director, said the current CCA has many pitfalls and the proposed amendments fail to safeguard the right to freedom of expression and the right to privacy.
The amendments would allow censorship and surveillance in the name of national security, practices that don't meet requirements under international law.
Section 8 of the draft, reviewing Section 14 of the current CCA, still allows criminal liability for acts of libel, he told a forum at the Foreign Correspondents' Club of Thailand.
It also imposes criminal penalties on anyone posting false information online that is deemed to cause damage to the public, national security, public security, economic stability or public infrastructure, he said.
Due to the vague nature of the term "false information", the bill could be abused by authorities as has already occurred in some lese majeste cases under Article 112 of the Criminal Code, he said.
Section 9 of the draft, which reviews Section 15 of the current CCA, makes ISPs liable for the comments and actions of users. Such intermediary liability is an incentive for broad censorship, said Mr Zarifi.
Paiboon Amonpinyokeat, a cyber law expert at P&P Law Firm and Electronics Transactions Development Agency, admitted the CCA he helped draft a decade ago was abused to file defamation suits.
Authorities have not received enough training and lack adequate knowledge about online activities and technological developments, rendering them unable to handle enforcement of the law, said Mr Paiboon.
He noted the amendments would eliminate the governments's ability to block any content regardless of its legality.
But other issues have emerged, including an attempt to handle copyright issues through the CCA, said Mr Paiboon.
The cyber law expert, however, said the NLA had taken note of public concerns related to the CCA amendments.
According to the Thai Netizen Network (TNN), the NLA extended the period to consider the amendments until next month.
The NLA should proceed with its second reading of the bill on Aug 26.
TNN coordinator Arthit Suriyawongkul was worried that ISPs would be required to take down third-party content without a proper judicial order.
"While proposed amendments to Section 15 allow for as yet undetermined conditions in which ISPs may evade punishment for acts by users, the burden of proof remains on them, which is not fair," said Mr Arthit.
"People have now asked if such amendments will jeopardise start-up businesses. I think they feel the pinch now, but don't have the power or a channel to communicate their concerns. If they do, there is no telling if authorities will listen to them," said the activist.