A New Haven activist group wants each city department to cut its budget by 10 percent to keep the city’s current tax rate in place next fiscal year.

So said Jeffrey Kerekes, one of the lead organizers of the New Haven Citizens Action Network, which has attended community meetings over the last several weeks to present an analysis of Mayor John DeStefano Jr.’s fiscal year 2010-’11 $670 million budget proposal. The group is collecting signatures for a petition to the aldermanic finance committee that would recommend the 10 percent cuts to the full board.

But while Kerekes, a psychotherapist and realtor who lives in the city, said group members are frustrated with the mayor’s proposal because it will increase city taxes, Ward 23 Alderman Yusuf Shah, the finance committee chair, said he thinks the 10 percent cuts would be irresponsible and decrease city services.

Kerekes said the 10 percent in departmental cuts would ensure that the city would not have to increase its taxes.

“The city needs to understand that people cannot afford this increase,” he said.

But the mayor’s budget proposal already asks for cuts across departments. Through the program, “Innovation Based Budgeting,” department managers will work to generate $8 million to the budget, or 1.7 percent in budget savings. City Hall spokeswoman Jessica Mayorga said in a e-mail Wednesday that the mayor’s cuts will decrease expenses and increase revenue to ease the tax burden on city residents.

Still, Kerekes said the program is not enough.

“We can’t afford to keep doing what we are doing,” he said.

New Haven Citizens Action Network supporters collected signatures across the city Wednesday night, Kerekes said. The petition generated 565 signatures online as of 7:49 p.m. Wednesday, and Kerekes said he did not know how many signatures had been collected on paper.

Residents also gathered Wednesday at the Harry A. Conte/West Hills Magnet School in Wooster Square to hear Kerekes give the group’s budget pitch.

Ward 26 Alderman Sergio Rodriguez, who attended the meeting at the school, said he wants to read the group’s petition more carefully and that he thinks the city needs to talk about increasing revenue in addition to making cuts.

“It has to go hand in hand,” he said after the meeting.

Thomas Ahern, 82, a resident of the Hill neighborhood who also attended the meeting, said that while he supports the petition, he thinks local residents should have meetings in their respective wards to discuss the budget.

But Shah said that instead of requesting broad budget cuts, citizens should talk with their aldermen and explain what specific cuts they want.

“The City of New Haven is not a Fortune 500 company,” he added. “You just can’t reduce costs and expenses [unilaterally].”

Kerekes — a member of the city’s Financial Review and Audit Commission, which is in charge of reviewing the city’s finances — said group members have talked with city officials but is not directly working with City Hall on budget reform.

Over the last month, the aldermanic finance committee has heard testimonies from city departments on how much funding they require. The committee will hold a public hearing on the budget April 28.