When Schools Chancellor Dennis M. Walcott stood in front of an elementary school on West 111th Street on Friday and stressed the need for the State Legislature to give him more authority to remove teachers for sexual misconduct, he knew it was an agenda that had very little chance of being addressed this year.

And when the United Federation of Teachers called for the City Council to investigate the city's hiring practices, it was trying to change the subject, from dangerous teachers to city bureaucrats.

The matter of teacher discipline has sparked a volley of debate and accusations over the last few weeks, an outgrowth of the contentious relationship between the teachers' union and the city.

But in spite of all the noise, there is little likelihood that Albany will be addressing the matter any time soon -- or that the matter will be resolved without legislative intervention, given the tension between the city and the union, according to people familiar with the issue.

The latest union-city brouhaha was set off late last month, when city officials announced that they were pushing a measure in Albany to give school system leaders, namely Mr. Walcott, the power to fire offenders, even if an independent arbitrator agreed upon by the Department of Education and the United Federation of Teachers decided on a lighter penalty.

The measure is being promoted as the city is hearing of a record number of complaints of sexual misconduct involving public school employees and students. There have been at least 10 this year. Both Mr. Walcott and Mayor Michael R. Bloomberg have pressed for the enhanced power as a necessary tool to protect children.

Sponsored in May in the Republican-controlled State Senate by Senator Stephen M. Saland, a Republican from Poughkeepsie, N.Y., the bill has found no sponsor in the Assembly, where Sheldon Silver, the Democratic speaker, maintains strong ties to the teachers' union.

The union fiercely opposes the changes, insisting that the arbitration system that was agreed upon by both parties and codified in the teachers' contract is sufficient. Further, they say, the system runs more efficiently and hands out more severe penalties in New York City than it does in other parts of the state.

The word-flinging escalated on Friday. Mr. Walcott stood outside Public School, 208, the Alain L. Locke School, where a third-grade teacher had been removed the day before and charged with sexually abusing an 8-year-old girl. Mr. Walcott told reporters that he hoped legislators could be pressured to drive the bill forward.

The news conference, which was preceded by a meeting inside the P.S. 208 auditorium with dozens of distraught parents, was one of several opportunities Mr. Walcott has taken in recent weeks to campaign for the legislation.

The chancellor has been on the radio, written an essay for the Op-Ed Page in The New York Times calling the current system a “recipe for disaster” and spoken often with reporters about the need for the change.

Asked why he kept promoting a dormant bill, Mr. Walcott said in a telephone interview on Monday that he wanted to keep the matter in the public eye. “My goal is to make sure people are aware of the issue,” he said.

But the United Federation of Teachers president, Michael Mulgrew, said he thought Mr. Walcott was using the legislation to batter the union. He is locked in several battles with the union: over the current teacher evaluation system, the Education Department’s school closing philosophy and now the fate of teachers at 24 schools scheduled to be shut and reopened with new names and revamped staffs.

Mr. Mulgrew also said he thought city officials were trying to distract parents from recent disappointments. This month, statistics on the city’s four-year graduation rate for the 2010-11 school year showed that the city had made little progress from the previous year: 65.5 percent of students graduated within four years, up from 65 percent the year before. So the rate has been almost flat despite Mayor Michael R. Bloomberg’s extensive efforts to close failing schools, turn around others and open smaller ones.

“I think it’s just a red herring to try to distract people,” Mr. Mulgrew said in a telephone interview on Tuesday.

In a letter Friday to Robert Jackson, chairman of the City Council’s Education Committee, Mr. Mulgrew said the union had “a zero tolerance” policy for sexual misconduct, which is why teachers accused of it are immediately removed from their positions and fired if they are found guilty.

In light of recent cases, Mr. Mulgrew wrote, the city ought to review whether its screening process is comprehensive enough.

The city has insisted that public school educators are thoroughly vetted with extensive screening and fingerprinting.

The problem, city officials say, is on the firing end, when teachers are accused of acting inappropriately yet find themselves back in the classroom.

The city has been working for more than a year to alter the teacher disciplinary process, testifying in Albany last May before the state Education Committee; officials insisted that the current system was inconsistent and relied too heavily on the whims of individual arbitrators.

Under the system, cases are handled by an arbitrator from a pool of applicants agreed upon by both the city and the union. The arbitrator is charged with hearing the cases and assigning penalties. In cases in which the arbitrator finds "inappropriate behavior,” a broad range of disciplines are permitted. But rulings of “sexual misconduct” require firing.

This winter, the Department of Education reviewed an estimated 240 misconduct cases, sexual in nature, said to have occurred since 2000. Mr. Walcott said he found fault with resolutions in 10 percent of the cases, determining that offenses deemed inappropriate by the arbitrator were, in his estimation, “sexual misconduct.”

In the interview on Monday, Mr. Walcott said these cases had “galvanized me even more.” And in a handful of them, he has moved to fire teachers.

In one incident, in 2007, a high school teacher was found to have touched the leg of one student and pressed his groin against the leg of another. The arbitrator ruled that the behavior “was wholly inappropriate and incompatible with the requirements of his teaching duties,” but determined that the incidents were not sexually motivated. The teacher was suspended for 45 days and then returned to the classroom.

In a 2008 incident, a teacher told a 13-year-old that “he loved her” and that she was in his dreams and he wanted to see her over the summer to tell her things “he couldn’t say in school.” The arbitrator ruled this was not “sexual conduct,” but rather “inappropriate conduct.” The teacher was reprimanded, returned to the classroom and received back pay for the period in which he was suspended awaiting his hearing.

And in another incident in 2008, a Bronx high school teacher was found to have tickled female students on their stomachs, rubbed their heads and told them another teacher had a "sexy butt.”

The arbitrator ruled that the teacher had acted “immaturely and inappropriately, but not in a sexual manner.” The teacher was fined $10,000.

In his New York Times Op-Ed essay, Mr. Walcott said the problem was that the independent arbitrators were hoping to keep their jobs, and so try to please all sides when issuing a verdict. And in doing so, Mr. Walcott said, the arbitrator will often be overly lenient.

But Mr. Mulgrew has said the union does not want arbitrators to reassign sexual offenders to the classroom. “If you are guilty of any sexual misconduct, you must be terminated,” he said. “That’s how seriously we take this.”

State Senator Jeffrey D. Klein, a Democrat who represents the Bronx and Westchester, said the system was clearly flawed. He said he hoped the Education Department and the teachers' union could work together to rectify it.

“I think this is a very important issue,” he said. “I think it’s important that the two sides settle it.”

Asked why the bill had not found a sponsor in the Assembly, Senator Klein said: “The teachers have a lot of allies in the Assembly. No one is interested in introducing the bill.”