PAWTUCKET — No source has been found for the $612,962 it will cost to expand full-day kindergarten from 2 to all 10 of the city’s elementary schools next year, school officials said during Tuesday night’s School Committee meeting.

School Supt. Hans W. Dellith, who said efforts are being made to identify a money source for the initiative, acknowledged none has been found.

“We don’t have the money. I know that,” Dellith admitted. “All I can say is we’re trying to look at the needs of the student and also keep the fiscal picture in sight.”

The statement came after John S. Baxter Jr., a School Committee member running for City Council, questioned the financial rationale that school officials used to back their recommendation that full-day kindergarten be instituted throughout the public school system.

At the school budget workshop last month, school business manager Thomas J. Conlon suggested that state reimbursement would be available for the initiative, and that the planned layoff of a librarian and seven elementary school teachers would offset its cost.

But the School Department is facing a $5-million budget deficit next year. In answer to questions from Baxter, Conlon acknowledged that the layoffs — which are due to declining elementary school enrollments — could be used to offset the deficit.

And he didn’t disagree when Baxter said the General Assembly doesn’t plan to replenish the state fund that provides reimbursement to schools with full-day kindergartens at the rate of $1,500 per pupil per year.

Pawtucket already receives $366,000 from that fund –– for the full-day kindergartens at the M. Virginia Cunningham and the Elizabeth Baldwin elementary schools.

Baxter, who is director of constituent services to Senate President Joseph A. Montalbano, said he has learned through his contacts in the State House that the fund that provides the $366,000 will be level-funded by the General Assembly, dimming any hope of increased state reimbursement next year.

Under the circumstances, Baxter said, the School Committee should reconsider the matter.

“I think we can now fairly say that it’s going to cost $612,000.”

“I want you to think about considering what we’ve done,” he said, addressing School Committee members. “We know that we’ve added $612,000 to a burgeoning deficit.”

The School Committee is in favor of full-day kindergarten because it increases the amount of time available for learning and Pawtucket, like every other school district in the country, is under pressure to boost student performance on standardized tests.

Under School Committee rules, as members who voted no on the matter, neither Baxter nor David A. Coughlin could seek another vote themselves.

Joanne Bonollo, who voted for full-day kindergarten, said she might follow Baxter’s suggestion and move to reconsider the matter, but not immediately. “At some point, it’s possible,” she said.

Bonollo said she voted for full-day kindergarten despite the apparent lack of money to make the initiative “a viable option.”

If she and other School Committee members hadn’t voted in favor of full-day kindergarten, the initiative would have been dropped, Bonollo said, with the school system’s financial difficulties being used as an excuse.

School Committee member James T. Chellel Jr., who also voted in favor of full-day kindergarten, said the program is so beneficial, he would never move to take it out of the budget.

Chellel accused Baxter of turning the matter into a political issue to bolster his bid for City Council at-large.

“It’s totally disingenuous to suggest that it was political,” Baxter responded. The concerns he expressed during Tuesday night’s meeting were no different from the objections he raised during the March 24 budget workshop, he said.

On both occasions, Baxter said, he was skeptical about the availability of financing for the program.

“I’ve been consistent ever since the proposal was brought up.”

In addition to Chellel and Bonollo, the full-day kindergarten initiative received the support of School Committee members Amy L. Zolt and Nicole A.. Nordquist, and Gordon M. Gould, the School Committee chairman.

Zolt couldn’t be reached for comment yesterday. Nordquist and Gould didn’t return calls.

jcastell@projo.com