The Labour leader, Andrew Little, said the rushed process was "appalling" and "sloppy" but the concessions had "balanced what was previously a very unbalanced piece of legislation".
The changes Labour secured in the select committee were significant.
Intrusive new surveillance powers will be permitted only in relation to terrorist activity, not the Security Intelligence Service's wider activities. Emergency, warrantless surveillance of suspects will be limited to 24 hours instead of 48 and subject to stricter oversight and more frequent reporting. And suspects who have their passports cancelled for three years will be able to appeal and apply to get them back.
Mr Little was asked if Labour had softened its stance on security, given it had opposed changes to the Government Communications Security Bureau (GCSB) last year.
He said the counter-terrorism bill was different because it had a sunset clause.
That expiry date for the interim legislation was brought forward by the committee to 2017, which means a full review of intelligence and security legislation will have to be completed in this parliamentary term.
New Zealand First leader Winston Peters said his party would not support the bill unless further changes were made at the committee stage.
He was uncomfortable with the speed at which it was being passed into law and wanted reassurances spy agencies would be "restrained" in their use of visual surveillance.
The Green Party said it would vote no because the Government had not made the case for the changes.
Co-leader Russel Norman said: "Unwarranted surveillance is still unwarranted surveillance even if it's only for 24 hours."
Speaking on TV3's Firstline this morning, Mr Little said that on balance, the party thought it should support the bill.
But he again criticised National's rushed process, saying Labour "fought for an hour in Parliament" for a delay to the introduction of the new legislation.
"People should always be sceptical when there are demands and plans for extra powers by security agencies that intrude on rights and freedoms, and when that happens there should be a decent amount of time for every citizen to have their say if they want to have it," he said.
"We're certainly saying the process is important, we don't ever want to see a repeat of it again, and I can promise you under the next Labour Government we would never allow legislation like this to be processed in this sort of way. But on this occasion we had to deal with the substance of the bill."
What does the bill do?
It targets New Zealand terror suspects associated with the Islamic State by giving authorities greater surveillance powers, the ability to cancel passports for a longer period, and access to Customs data.
What changes have been made?
Emergency, warrantless surveillance will be allowed for only 24 hours, not 48 hours. Warrantless surveillance and new provisions for visual surveillance on private properties can be used only in relation to the "foreign fighters" threat and will be subject to greater oversight and six-monthly reporting. The measures expire in 2017.
Why were these changes made?
MPs expressed discomfort with the reach of the changes. There was also resistance from Islamic groups, the Law Society, the Human Rights Commission and others.
Who will support the bill?
National, Labour, United Future, and Act are backing it. Greens oppose it, as do New Zealand First if there are not significant changes. The Maori Party is undecided.
