It says that any department could be added in the future by order in council - regulation - which is the decision of just the cabinet and not the Parliament.
Mr Peters' support is not required for the bill but he is likely to support it if he can get the changes he wants.
Other opposition parties are refusing to support it under any circumstances, with Labour and Greens calling for an inquiry into New Zealand's intelligence agencies.
The Government Communications Security Bureau and Related Legislation Amendment Bill was introduced to Parliament yesterday and passed its first reading by 61 to 59. National had the support of only Act and United Future.
Mr Key wrote to Mr Peters on Monday about the bill offering him a briefing on it and a meeting if he chose.
Mr Peters replied yesterday setting his party's objections and he has not taken up the offer of a meeting.
Mr Key has insisted that the bill does not expand the activities of the GCSB but clarifies its legal ability to work in the way it has for years, including under the last Labour Government.
Labour leader David Shearer told Parliament the bill was "a patch-up job" on an intelligence network that had some very serious shortfalls.
"This is about our national security; it is about our human rights; it is about Kiwis' confidence in the integrity of our intelligence agencies."
He wanted a wide independent inquiry across the intelligence agencies, rather than focusing on the workings of the GCSB.
"We need to do this properly, we need to do it once and we need to get it right because we can't go on as we are."
Greens co-leader Russel Norman said the parliamentary oversight of the GCSB and other spy agencies had been woeful.
"Is it any wonder that these agencies living under a stone for three or four decades with no public scrutiny, no sunlight ever exposed to them went dysfunctional.?
A review of compliance by cabinet secretary Rebecca Kitteridge found that New Zealanders may have been spied on unlawfully up to 88 times.
The bill will be considered by the Intelligence and Security Committee and will be reported back by July 26.
Because the process has been shortened from six months to four months, the first reading debate was open ended and the Government took it under urgency.