New Haven Mayor John DeStefano Jr. met Aug. 30 with the union for the University Police, and agreed to help resolve the ongoing dispute over new police contracts — now in its third year.

The two sides have not met since June, when a settlement seemed close before talks eventually broke down. The Yale Police Benevolent Association — which represents 55 officers — wrote to the mayor in July requesting that he act as a mediator, and met with him in City Hall for an hour Monday, YPBA chief steward Christopher Morganti said.

University Deputy Secretary Martha Highsmith said Yale would welcome the assistance of the mayor.

“We are open to assistance from any quarters to move the contract negotiations along,” she said.

DeStefano downplayed the role he will play in the discussions, saying he would try to bring the sides together but would not take part in negotiations. The mayor stepped in to resolve the YPBA’s last contract talks in 1998, when the union came close to striking. He also worked last year to settle contracts between the University and locals 34 and 35 — its two largest unions.

Morganti said he was pleased by the meeting with DeStefano, calling the mayor “very knowledgeable.” The union has been critical of the federal mediator brought in by Yale, Joseph Dubin, whom Highsmith said would be present at a planned contract negotiation at City Hall next week.

DeStefano expressed optimism that the conflict between the two sides could be resolved.

“As opposed to my involvement in the 34-35 negotiations, I think the two sides are fairly close,” DeStefano said. “I think it is resolvable if both parties apply themselves anew to this effort.”

Yale and the YPBA seemed close to a resolution as talks wound down in June. Morganti said union leaders spent three hours in caucus before the last talk, and came up with several new proposals. Highsmith said the University made several last-minute concessions — including agreeing to the union’s request for a 2.5 percent pension multiplier. The sides also agreed on an eight-year contract, as well as changes in retirement age and a new work schedule, she said, but did not reach a final agreement.

Morganti blamed some of the lack of progress since June on the University’s refusal to budge on the issue of disciplining officers. Highsmith said the current system of discipline has proven to be effective and does not need to be changed.

“We’ve been clear that an erosion of management rights in this area is something we feel is neither necessary nor appropriate,” she said. “The chief of police has to have the ability to run his department.”

Since the last union contract expired 26 months ago, the two sides have been renewing their contract on a monthly basis. Either side can choose to cancel the contract, which would open the way for job actions — including a possible strike.

As long as talks with the mayor are continuing, Morganti said the YPBA would not cancel the contract. But he said union members would consider leafletting during Parents’ Weekend in October — as they did last year — unless progress was made.