The test for warrantless surveillance of suspects should be strengthened and the surveillance should be limited to 24 hours instead of 48 hours.
The sunset clause for the bill should be October 2016 instead of October 2018.
Sir Geoffrey said an earlier expiry date would incentivise completion of a wider review of security and intelligence laws which was due to start next year.
The Law Society also criticised the rush to pass the bill before the end of the year.
"It is highly undesirable to pass legislation of this nature under urgency."
SIS head Rebecca Kitteridge has briefed the select committee considering urgent "Freedom Fighters" legislation in private session this morning.
Ms Kitteridge emerged to tell waiting media that it was a "useful session" and while she understood the concerns some of the MPs had, she believed the legislation was necessary.
She refused to say in detail what she had told the MPs, but said she had tried to answer their questions about the circumstances New Zealand faced and give some examples of the need for the legislation.
"They've got a deep interest in this legislation, to make sure that it is fair and needed. And I totally understand that. So I was happy to answer the questions they had."
The bill will allow the passports of suspected freedom fights to be suspended for up to three years and extend the surveillance powers of the SIS - including allowing them a 48 hour window to conduct survelliance without a warrant.
The bill is being rushed through under urgency by the Government and its public submission phase is extremely truncated.
Ms Kitteridge said the SIS had input into the bill. "You can be sure we think it is necessary.
"As people can see, the threat level in New Zealand has been raised and the context justifies these extra provisions."
The committee is expected to go into public session to hear submissions from groups including the Muslim Association, Law Society and Privacy Commisson.