It is opposed by National and Act and will not progress without NZ First's support.
The Government had intended for the bill have its committee stage in the House this week, but it has been pushed back by at least one week.
A spokesman for Leader of the House Chris Hipkins wouldn't comment on whether that had anything to do with NZ First's position on the bill.
"We're on track to pass the Arms Legislation Bill this sitting block," the spokesman said.
A spokeswoman for Peters confirmed that an email in Cahill's name landed in Peters' inbox urging him to oppose the bill, but it was disregarded as Cahill's position on the bill was well known.
She said it was one of thousands of emails generated from Colfo's email form, which was being sent to all NZ First MPs.
Colfo spokeswoman Nicole McKee said she hoped that any politician receiving such an email in the name of Chris Cahill would recognise it as "someone doing some foul play".
"It's really unfortunate that's he's been used in this way. It's certainly not something we condone."
Peters has not said if NZ First will continue to support the passage of the bill, saying only in a statement that he is discussing it in caucus and with its coalition partner.
The bill has been more universally opposed by hunting, fishing, farming and recreational shooting groups than the first tranche of gun law reforms, which outlawed most military-style semi-automatic firearms.
The National Party has proposed several amendments to the bill, including scrapping the register and having exemptions for using certain firearms for shooting competitions and farming pest control.
National's police spokesman Brett Hudson said he had had no conversations with NZ First about whether the party might support any of his proposed amendments.
Cahill said the passage of the bill would improve public safety and reverse the decades of political neglect on gun law reforms.
"For 30 years, politicians have failed the memory of the Aramoana massacre victims, and the Police Association is asking them to, this week in Parliament, avoid adding the victims of Christchurch to that legacy," he said.
"What that means is putting aside political point-scoring and stepping up to pass the Arms Legislation Bill, which is the right thing for the safety of all New Zealanders."