Internment in the North is not an option, according to the president of the Alliance Party, Dr Philip McGarry.
He urged that the effectiveness of any new security measures be carefully monitored.
Dr McGarry stressed that underpinning any action on security should be the due process of law and natural justice, which he called the cornerstones of any democratic society.
"We have always taken the view that the most effective way of dealing with terrorists is through the community providing the police with information about acts of violence."
A reintroduction of internment would be a distortion of these principles and would, he believed, "undermine the struggle of our community against the onslaught of terrorism."
An Alliance councillor in Belfast, Mr Tom Campbell, has also issued a word of warning on potential problems with the legislation.
The possibility of a court being able to cross-examine a senior police officer on the basis of his belief that a defendant was a member of an illegal organisation represented a particular concern for Mr Campbell, a solicitor.
"This could open very sensitive security information, such as informer knowledge, which may then have long-term drawbacks on the fight against terrorism," he said.
The Deputy First Minister, Mr Seamus Mallon, has said the new anti-terror laws must be specifically targeted and used effectively to achieve the intended effect. This is something fully understood by both governments, he said.
Responding to a question posed on the negative fall-out in the North of tough security measures in the past, Mr Mallon said: "I believe all emergency legislation should, by definition, be short-term measures."
The Sinn Fein chairman, Mr Mitchel McLaughlin, has described the anti-terrorist laws outlined by the British Prime Minister, Mr Tony Blair, as a panic measure which "in a very fundamental way attacks the whole system of democratic accountability."
He said: "The result of such repressive legislation has historically been the routine violation of human and civil rights.
"Full implementation of the Good Friday agreement plus public opinion will do more to prevent a recurrence of the tragic events of Omagh than will any repressive security response."
A statement issued by the 32-County Sovereignty Committee said the organisation believed repressive security measures never succeeded in the past and served only to make republicans more determined to end British rule.
"Such laws were always enacted, it was claimed, `temporarily' in the emotional aftermath of tragic events but were extended and became permanent," the organisation said.
Referring to what it saw as the setting up of a "police state" in the Republic, the statement continued: "The proposed new laws, particularly those intended for the South, would basically make a trial a nullity since the opinion of those making the arrests could not be challenged."
The movement concluded with the assertion that it is "determined that such tactics must not be allowed to succeed."
The Rev Ian Paisley, leader of the Democratic Unionist Party, has welcomed the security measures but stressed that they do not go far enough. "It's quite clear the Provisional IRA has nothing to fear from this legislation. It is a two-tier system of dealing with terrorists," he said.
Meanwhile, Families Against Intimidation and Terror (FAIT) has called for the new security measures to be used against paramilitaries involved in "punishment" attacks. The spokesman for FAIT, Mr Glyn Roberts, has said he is frustrated at the recent spate of punishment violence and believes the proposed security measures offer the governments a new opportunity to take action.
"Those paramilitaries who are involved in beatings, shootings and intimidating people should be brought to justice for their atrocities," he said.