A new report by the city’s chief financial officer that puts the city’s fiscal 2007 surplus at $5.6 billion is increasing calls for Mayor Bloomberg to sign off on steeper tax cuts.

Comptroller William Thompson Jr.’s estimate is $1.2 billion more than Mr. Bloomberg’s projection, which he unveiled last month when presenting the city budget.

While Mr. Thompson, a likely 2009 mayoral candidate, praised Mr. Bloomberg for using the surplus to plug out-year budget gaps and invoking fiscal prudence, others said the ballooning surplus provides even more evidence that it is time to return money to the taxpayers.

“It’s evident now more than ever that we need to provide deeper property tax relief than was earlier proposed,” the City Council’s Republican minority leader, James Oddo, said. “My constituents are paying 60%, 70%, and, in some cases, 80% more in property taxes today than they were five years ago.”

Mr. Oddo was an ardent opponent of the property tax hikes Mr. Bloomberg pushed through after the World Trade Center attacks. He recently wrote a letter to the mayor requesting that half of any surplus above the $4.4 billion projected be used to provide additional property tax relief.

Mr. Bloomberg has already written a one-year, $1 billion tax cut package into his budget. That includes $750 million in property tax relief. While the property tax cut is a one-year proposal, Mr. Bloomberg has said he would extend it if the economy holds up. He also backed a lowering of the city’s sales tax and cuts to a number of small business taxes.

It was unclear last night whether Mr. Thompson’s $5.6 billion surplus projection included the money Mr. Bloomberg has already set aside to pay down long-term public debt. Mr. Thompson’s office did not return calls for further explanation.

After the mayor presented his budget last month, several council members disputed the surplus figure he used, saying a more accurate reading of the surplus would have include the money set aside for debt payments. Downplaying the surplus and stashing away money for the future helps Mr. Bloomberg justify his plan even in the face of calls for more tax cuts or for additional spending. Budget watchdogs have called him fiscally prudent.

In his report, Mr. Thompson projected that the “steadily growing economy,” would mean a continuation of strong tax revenues that will reduce budget gaps even more than Mr. Bloomberg has done.

Mr. Bloomberg has repeatedly said that his plan is the most fiscally prudent because the city’s fixed expenses — such as its pension payments to municipal employees — are skyrocketing.

Mr. Thompson noted that growth rates several of those fixed expenses have “begun to moderate.”

“Pension costs, which escalated after investment losses in 2002 and 2003, are expected to remain relatively flat starting in” fiscal year 2009, a summary of his report stated.