Among the 36 changes being recommended by the bipartisan parliamentary joint committee on intelligence and security are that police and spy agency powers to hold people without charge or restrict their movements should expire two years after the next federal election – significantly sooner than the 10-year sunset clause the government is seeking.

The committee also calls for greater oversight of another controversial measure, that of the Foreign Minister's ability to declare a terrorist hotspot a "no go zone", making it a crime to travel there without an innocent reason.

It says whole countries should not be declared terrorist zones – only particular regions – and each declaration should be a "disallowable instrument", meaning it can be overturned by either house of Parliament. Also, that the law should have a sunset clause at 24 months after the next election.

And it recommends the bill should more clearly define what is meant by "advocating" terrorism – which would become a crime under the new law as distinct from the current crime of inciting terrorist acts, which is considerably more specific. Muslim groups and lawyers have protested that legitimate debate could be criminalised because the current wording of the law is far too broad.

On the whole, the committee has backed the thrust of the bill, largely calling for elements to be watered down or for additional oversight to be applied, rather than measures scrapped altogether.

Attorney-General George Brandis said he would consider the recommendations of the committee, but repeatedly told ABC radio on Friday the changes were "relatively small".

"They do not suggest that any of the principal measures in the bill not be proceeded with and the government is glad about that and, secondly, the recommendations that are made do seem to me on a cursory reading to be very much at the margin," he said.

Shadow attorney-general Mark Dreyfus similarly kept his powder dry, but indicated that if the government followed the recommendations of the committee, Labor would be well-disposed towards the laws.

"At this point, provided the government agrees to the recommendations and provided the government brings forward satisfactory amendments … and gives the explanations that the committee recommended, I think we could get to a position where Labor will be able to support the bill," he said.

While that leaves open the possibility Labor would withdraw its support, the fact the committee included senior representation through its deputy leader Tanya Plibersek, as well as frontbench senators Penny Wong, Stephen Conroy and former defence minister John Faulkner, means that is unlikely.