Sinn Fein and SDLP MLAs voiced their objections to several proposals contained within the Justice Bill, on 6 December 2012.
Speaking at a meeting of the Justice Committee, Raymond McCartney of Sinn Fein expressed particular opposition to parts of the bill relating to the police retention of fingerprints and DNA material.
"We have severe reservations," he said.
Mr McCartney said his party would be bringing a number of amendments at the further consideration stage of the bill.
Alban Maginness of the SDLP said his party shared Sinn Fein's concerns and would consider supporting the amendments.
The committee then heard from Prison Service (NIPS) officials on consultation responses to the NIPS Outline Estate Strategy.
Justice Minister David Ford briefed the Assembly on 26 November 2012 on his preferred options for the prisons estate, when he expressed a preference to retain the existing prison at Magilligan.
NIPS Director General Sue McAllister told the committee the estate strategy was "a key element" in the prison reform programme.
She reiterated much of the information provided by the minister in his statement, including the decision to split Maghaberry Prison into three mini prisons, to provide separate secure accommodation for women, and to establish a "secure college".
The committee also heard a briefing from Department of Justice officials on the use of victim personal statements in criminal trials.
At the start of the meeting, committee chairman Paul Givan condemned the overnight attacks on the homes of Alliance Party members, and the destruction of the party office of committee member Alliance MLA Stewart Dickson.
He said the committee "supports the rule of law being upheld" and that the attacks were "a step too far".
Alban Maginness of the SDLP said the destruction of Mr Dickson's office was "an attack on all of us around this table".
Ulster Unionist Tom Elliott said "there is nothing that excuses the breaking of the law".
Mr McCartney said he had spoken to Mr Dickson following the attack.
"We are all united in our support for Stewart," he said.