Finance Minister Bill English has rejected a union call to make job protection a condition of the Government's bank guarantee schemes.
Finsec says banks and other financial institutions joining the retail deposit or wholesale funding guarantee schemes, should in return commit to retaining current staffing levels.
It delivered a petition, with 10,000 signatures, at Parliament on Tuesday.
But Mr English says there's no prospect of the Government removing a bank's guarantee if jobs are cut.
He says it's heavy-handed and the removal of a guarantee from a major bank could affect thousands of jobs.
Finsec has also released a survey which it says shows public support for forcing banks to maintain their current staffing levels.
In a UMR Research survey conducted last month, respondents were asked if the Government should require banks to maintain existing staffing levels and not send jobs overseas. It revealed that 79% said yes, and 14% said no.
Finsec's campaigns director Andrew Campbell says New Zealanders want the government to be active in protecting local jobs.
But the Bankers Association is objecting to the Finsec petition.
A spokesperson for the Association John Bishop says it would be wrong to impose additional conditions on the banking agreements which have been in place for several months.
He also says it's unfair for the union to represent the deposit guarantee scheme as taxpayer support, when banks and their customers are paying fees to be part of it.
The deposit guarantees were designed by the previous Government and announced in October and November last year.