A parliamentary official confirmed on Wednesday that meetings scheduled for the next week were scrapped to give political parties time to deliberate on the way forward.
The chairperson of the ad hoc committee, Raseriti Tau, will now seek an extension of the lawmakers' 22 June deadline to report back to the National Council of Provinces.
The move comes after government on Tuesday objected to amendments proposed by the ANC in May, in response to sustained criticism of the bill and threats to take it on constitutional review.
The department of state security rejected proposals by the ruling party to give greater protection to whistle-blowers, to remove all minimum prison sentences from the bill and to narrow the definition of national security.
Acting director general of state security, Dennis Dlomo, said the term needs to be broadly defined to allow the government to use the legislation to respond to emerging threats.
He also dismissed a proposal by opposition parties to delete a provision that the new classification law would trump the Promotion of Access to Information Act if the two came into conflict.
Critics have repeatedly warned that the provision, contained in section 1(4), is patently unconstitutional.
Rights groups cautiously welcomed the ANC's proposed amendments last month, but urged the ruling party to go further and include a public interest defence for those charged with revealing state secrets.
The ANC's MPs made a gesture in this direction by proposing that people who reveal classified information to expose criminal wrongdoing be exempt from prosecution.
However, the department also rejected this amendment, along with the ANC's stated readiness to remove clauses that would, according to legal experts, place an unacceptably heavy onus on those charged under the legislation.
The director of the Open Democracy Advice Centre, Alison Tilley, said the department's attempt to prescribe to lawmakers was problematic.
"There's clearly an attempt from the executive branch of government to tell Parliament how it should and should not legislate, which demonstrates a clear misunderstanding of the doctrine of separation of powers."
The bill was passed by the National Assembly late last year amid threats of legal challenge unless it were significantly rewritten.
The ANC then embarked on a process of public consultation in provinces and in March held renewed public hearings, where presenters from veteran rights lawyer George Bizos to Cosatu general secretary Zwelinzima Vavi warned it would be struck down by the Constitutional Court.