CRANSTON –– School Department lawyers met with Mayor Michael T. Napolitano and his top aides yesterday afternoon as the two sides attempted to head off a costly legal battle over local support for education.

City and school officials said the meeting was cordial, even “productive,” but reported no breakthroughs.

And School Committee Chairman Michael A. Traficante said the district will sue City Hall for $4.9 million, in what is known as a Caruolo action, if they cannot work out an agreement in a follow-up meeting tentatively scheduled for Friday.

“I think Friday is the drop-dead date,” Traficante said.

School officials say the district will run out of money before the fiscal year ends, on June 30.

And with that in mind, the School Committee authorized the Caruolo action last week.

The committee, angling for an out-of-court settlement, has not yet filed the lawsuit in Superior Court.

But all signs seem to be pointing to a courtroom confrontation.

The City Council met Saturday morning in what school officials hoped would be a last-minute attempt to find some cash for the schools in a tight budget.

But in an 8-1 vote, with member Jeffrey P. Barone in dissent, the council approved a non-binding resolution that essentially rejected the push for a settlement.

The committee called on Napolitano to seek a court order requiring the district to live within its $125.3-million budget for the current fiscal year.

Council President Aram G. Garabedian said the school district should have moved, from the start of this fiscal year, to contain costs.

School officials say they have attempted to tighten the belt over the course of the fiscal year. But they say binding labor contracts and unfunded mandates from the state and federal governments limited their ability to tweak the budget.

And they say they warned, from the beginning, that the $125.3 million in federal, state and local aid would not be enough to pay the bills.

Indeed, talk of a Caruolo lawsuit has been swirling for months.

And by January, school officials were projecting a $3.8-million shortfall and pushing the city to make up the difference.

The number has swelled to $4.9 million in recent weeks, officials say, as the district factors in rising utility costs and an estimated $250,000 in legal and consulting fees should the matter wind up in court.

The schools have already assembled a team of consultants and lawyers to press the Caruolo matter.

Former West Warwick School Supt. Thomas Sweeney and school finance expert Walter Edge have spent months combing through the district’s budget.

And lawyers Benjamin Scungio and Ronald Cascione, of the Providence firm Brennan, Recupero, Cascione, Scungio & McAllister, have been building the district’s legal case.

But Scungio, in an interview yesterday, said he hoped to avoid a costly trial.

He said his firm had been able to avert full-blown Caruolo lawsuits twice in North Providence and once in Johnston in recent years.

And the lawyers took the lead for the School Department in the meeting yesterday with Napolitano; the mayor’s director of administration, Ernest J. Carlucci; his finance director, Corsino Delgado, and City Solicitor Vito L. Sciolto.

Carlucci called the meeting “productive.” But he suggested there was little movement on either side.

District officials, in recent days, have suggested they cannot be terribly flexible on the $4.9-million figure.

And city officials have remained cool to the idea of raising taxes or dipping into the city’s reserves to finance a settlement with the schools.

But addressing the projected $4.9-million shortfall is but one step in dealing with the schools’ fiscal woes.

The district is also predicting a $7.4-million budget hole for the fiscal year that begins July 1.

dscharfe@projo.com