He said Datuk Seri Najib Razak's reforms were only beginning, and called on the prime minister to repeal or amend laws used to restrict printing and publication, student participation in politics, unions, public assembly and overseas voting.
"I and the opposition Pakatan Rakyat (PR) ask Najib to continue from here... Najib must seek to end all repressive laws with no reservations immediately," he said in a statement.
Anwar said that while the new Security Offences (Special Measures) Bill tabled yesterday was "commendable", PR still had reservations that the proposed law gave too broad powers to authorities to detain suspects.
This was in line with the Malaysian Bar's objections to the Bill, one of two laws meant to replace the draconian ISA, he noted.
The PKR de facto chief nonetheless said the move to abolish the ISA, which critics have said was used to imprison political opponents, was worth "celebrating".
He further claimed that Najib only moved to strike the archaic security law from the books due to persistent efforts by the opposition and civil society groups like Gerakan Mansuh ISA (GMI) and Suara Rakyat Malaysia (Suaram).
"Before this Bill's introduction, the opposition coalition had already pledged to abolish the ISA when it wins in the impending general election...
"Our ability to force the government’s hands was reinforced by Pakatan Rakyat gains in the general election in 2008," he said.
Anwar added that the world must not forget the damage ISA has wrought on many thousands of Malaysian detainees and their families over the past several decades, which "will (forever) remain a scar".
The ISA replacement law was tabled in the Dewan Rakyat yesterday, removing the government's option to detain without trial and providing a maximum detention of 28 days for investigation purposes.
Under the ISA, an individual believed to have committed a security offence can be detained for up to two years without trial, on orders from the home minister.
The Security Offences (Special Measures) Bill, tabled for first reading by de facto law minister Datuk Seri Nazri Aziz, states that "all security offences shall be tried by the High Court".
The new law also notably states that no individual can be arrested solely for his political belief or any political activity, as promised by Najib in September last year when he announced a raft of reforms aimed at increasing civil liberties.
But the Bill, the first of two laws that will replace the ISA, still allows the police to arrest and detain "any person whom he has reason to believe to be involved in security offences" without warrant for 24 hours for investigation.
The Malaysian Bar has criticised the Bill for its wide definition of security offences and its "radical departure" from ordinary rules of evidence, which may negatively impact on the accused's right to a fair trial.