"In the current, difficult economic times I am committed to maintaining that level of overall increase as a maximum.
"This means there has to be the difficult process of selecting some requests for funding and refusing others."
His budget changes propose $7.5 million more in rates revenue.
One project bounced off this year's list is the Auckland Harbour Bridge Pathway.
Mr Brown said he supported the idea but thought it needed more work before the council could consider whether to support it.
The request by Auckland Transport for an additional $9 million of rates funding for integrated ticketing could be reduced to $2 million, he said.
"I am fully committed to the implementation of the integrated ticketing project but I have communicated to Auckland Transport our inability to meet the full costs of this project."
He suggested a soft solution to achieve one of his pet projects - free access to swimming pools for everyone across Auckland. He failed to get council support for more than just children free and disabled swimmers missed out too.
The new plan is to seek commercial sponsorship for the council's 24 pools and use this money to give free access to the disabled, elderly and "potentially the Auckland community".
Responding to law changes in liquor licensing would add $1.4 million to the budget.
Mr Brown said the council had little choice and he hoped it could recover costs through setting appropriate fees in future years.
However, his proposed rates increase did not impress representatives of Auckland's eastern suburbs last night.
Orakei Local Board chairman Desley Simpson said: "The bank of Orakei gets robbed again.
"No new investment projects and no thanks for the tens of millions of dollars Orakei ratepayers contribute to the eftpos card that Len Brown uses for his shopping list supporting other areas of Auckland."
Councillor Cameron Brewer said an average 2.9 per cent rates rise was a complete misnomer.
More than 60 per cent of Orakei Ward residents were stung with 10 per cent rises last year and would face a similar rise this year.
Mr Brewer said the mayor had "gone soft" on the council-controlled organisations' spending while denying more cash for projects suggested by local boards.
He questioned the proposal to give Auckland Transport more money for integrated ticketing which had already cost ratepayers and taxpayers more than $100 million.
Average rates rises
5.7 per cent2005-06 to 2009-10 for eight councils
9 per cent 2010 transition authority forecast
3.9 per cent 2011-12
3.6 per cent 2012-13
2.9 per cent (proposed) 2013-14
6.8 per cent 2002-12 national average rise
Source: Auckland Council