Veterans for Peace, a national veterans’ group that has organized a second St. Patrick Day’s parade following the traditional parade in South Boston, is crying foul because, it says, the city has backed out of an agreement this year not to run street sweepers between the two parades.

The group asked a federal magistrate judge today to issue an emergency ruling ordering the city to abide by the agreement.

The judge, who has been presiding over the case for years, didn’t immediately issue a written ruling but said from the bench that, despite the city’s interpretation of one of his previous rulings, he had never meant to order the sweepers to roll between the two parades.

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Veterans for Peace says that running the sweepers signals that the city favors the traditional parade, which is run by the Allied War Veterans Council, over theirs. The dust and dirt raised by the sweepers also drives spectators away from the second parade, the peace group says.

“The effect ... was to demonstrate that the officially approved event had concluded and that spectators should leave,” Patrick Scanlon, coordinator of the Veterans for Peace, Chapter 9, Smedley Butler Brigade, said in a sworn statement attached to a federal court filing.

“By discouraging persons from participating in the Veterans for Peace Parade, the City of Boston diluted the First Amendment message of the Veterans for Peace,” the statement said.

The mayor’s press office didn’t immediately return a message seeking comment this afternoon.

Veterans for Peace organizers told the Globe earlier this month that the St. Patrick’s Peace Parade, which would include marchers from a gay rights group, would be bigger and better this year than last year, when it drew 2,000 people. Scanlon has said that the traditional parade is “a military parade hiding behind St. Patrick’s Day” and the second parade sends a needed “message of peace.”

In 2003, Veterans for Peace, which works to “build a culture of peace by using our experiences and lifting our voices,” according to its mission statement, organized a small parade and marched behind the traditional parade. The Allied War Veterans Council objected, saying the second parade violated a Supreme Court decision, the Globe reported.

US Magistrate Judge Robert Collings ruled in 2004 that the second parade could happen as long as it remained one mile behind the “police escort and street sweepers ... following the last authorized unit of the parade.”

Collings said today in US District Court in Boston that he hadn’t meant to order that the street sweepers go between the two parades. But he didn’t immediately agree to change the language of the order, and he took the matter under advisement.

Veterans for Peace said the city had agreed with the group last month not to run the street sweepers and not to take down crowd barricades — another action that the group says signaled to people the end of the official parade.

But on Friday, the city, citing the 2004 ruling by Collings, informed the group that, while it would leave the barricades in place, it would deploy the street sweepers.