But Mr Brown and Ms Hulse have confirmed to the Herald support for the review being extended to cover local body representatives.
"At a time we are trying to keep average rates increases as close to the rate of inflation as possible, this makes absolute sense," Mr Brown said.
The mayor received a pay rise of 3.4 per cent last year to take his salary to $259,500. Councillors had a 3.3 per cent bump to $101,900.
The consumers price index rose 1.5 per cent over that time.
The Remuneration Authority will in June announce how much those salaries will increase from July this year. Its decision to raise MPs' pay by 5.5 per cent - 3.5 per cent once a reduction in travel entitlement is factored in - set off anger when announced last week.
Mr Key, who said he was disappointed with the decision, will change the law to remove the authority's discretion when setting MPs' pay.
The sole criterion will be the average public sector pay increase for the previous year.
Yesterday a spokesman for Mr Key said the Government had no intention at this stage of widening the law change.
However, Howick councillor Dick Quax said he encouraged that decision to be reconsidered.
"I can't speak for other councillors, but Auckland councillors are pretty well paid for the job that they do."
Wellington mayor Celia Wade-Brown said she was keeping an open mind on the remuneration issue. "I am interested in a fair system, and one that works nationwide," the mayor said.