With the clock swiftly running down, Boston Mayor Martin J. Walsh said today that he would make one more attempt to resolve a standoff over whether a group of gay military veterans will be able to march in the St. Patrick’s Day parade on Sunday in South Boston.

“I am going to make one more pitch at it and we’ll see what happens,’’ Walsh said after a news conference today on another subject.

The mayor has been trying to find a middle ground between the South Boston Allied War Veterans Council, which sponsors the parade, and MassEquality, a statewide gay rights group. The two organizations have been at loggerheads over whether gay veterans can march openly in the parade.

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In trying to broker a deal, Walsh had sought small victories in a controversy that spans 20 years. Parade organizers said gay individuals can participate in the parade, which celebrates Irish culture and the Revolutionary War. But parade officials said they always exclude any activist groups during the march, a policy supported by the Supreme Court.

Walsh did manage to get the parade sponsors to invite MassEquality, which had filed an application to allow 20 gay veterans to march. But the sponsors wanted to require that the marchers not make any reference to their sexual orientation on T-shirts or signs. MassEquality said it could not abide by those conditions.

Parade sponsors rescinded their offer, contending that MassEquality had lied in its application about the number of veterans who would march as a “ploy” to participate in the event.

MassEquality responded Wednesday with a letter to parade organizers signed by 12 gay war veterans, but later the group’s executive director said all talks were off.

With three days to go before the event, Walsh said he would attend the annual St. Patrick’s Day breakfast, which will feature its first black host when state Senator Linda Dorcena-Forry, a Haitian-American from Dorchester, takes the microphone.

The mayor said he may also hit a couple of parties in South Boston, but unless MassEquality marches, he will not be participate in the parade.

“We pretty much have an agreement in principle,’’ Walsh said of MassEquality and parade sponsors. “But I think it is a little bit of stubbornness and a little bit of outside influences on both sides that need to take a step back and let us come up with an understanding here.”