Without changing the law, something the authority had already asked the Government to do, there was no guarantee the authority would follow Mr Key's wishes, Mr Goff said in an interview.
Mr Key, in a letter to authority chairman David Oughton, said the New Zealand economy, like that in most countries, was facing what looked to be a difficult period.
"Accordingly, it is the view of my Government that the Remuneration Authority should exercise restraint when considering salary determinations for those persons within its jurisdiction."
At the appropriate time, the National Party would file a submission recommending a zero increase for parliamentary salaries, he said.
Mr Key, who is worth an estimated $50 million, is already known for giving part of his parliamentary salary to charity.
Economists are predicting inflation will reach zero by September.
Wage inflation is also expected to fall quickly this year as New Zealanders face lower wage rises from businesses struggling to survive in a recession.
MPs' salaries are expected to be reviewed again in November.
There was outrage late last year when the authority increased judges' pay by 4.8% and MPs salaries by between 3.8% and 4.8% at a time when the country was facing a deep, prolonged recession.
Mr Key said yesterday it was only right that in these changing economic times, as "ordinary New Zealanders" tightened their belts, MPs and ministers also played their part.
The authority was an independent body, but Mr Key hoped it would recognise the economic climate called for a cautious use of taxpayer money.
The Government was committed to getting New Zealand through challenging economic times and on a path towards better economic growth.
It was implementing its economic plan and more initiatives would be coming next month.
Mr Goff said the requirement for the authority to take "fairness to taxpayers" into consideration did not make it clear enough that when it was setting salaries it should take general economic circumstances into consideration.
"There needs to be an explicit direction to take the economy and the general circumstances of other New Zealanders into consideration.
You can't do that without changing the law."
Labour would support a change in the law and he urged Mr Key to seek cross-party support for a law change.
