Mayor Martin J. Walsh was head of the Boston Building Trades from 2011 to 2013.Lane Turner/Globe Staff/File 2014/Globe Staff

Labor leaders and elected officials reacted cautiously Sunday to news of a far-reaching federal probe of organized labor that includes Mayor Martin J. Walsh’s time as a union official.

Walsh received a standing ovation at a breakfast fund-raiser in East Boston packed with hundreds of supporters including union members. In a telephone interview, Steven A. Tolman, president of the Massachusetts AFL-CIO, declined to comment on the investigation, which is examining whether labor officials threatened developers and businesspeople who hired nonunion workers.

Recalling working with Walsh in the state Legislature, Tolman said, “At all times, his integrity was impeccable. I’ve very proud that we got him elected mayor of the city because I think he has the people of Boston’s back.”

But while Walsh will be buoyed by his strong popularity, he could be haunted by his refusal to address many specifics about the investigation, said Peter N. Ubertaccio, a political science professor at Stonehill College.

The mayor, who promised to usher in a new era of transparency at City Hall, would not say in an interview with the Globe whether he has appeared before a grand jury.

“If you can’t answer that question you are only inviting greater scrutiny,” Ubertaccio said Sunday. “Those are tactics of old Boston that are not looked upon fairly in the new era.”

Walsh’s administration will not say how many staff members have been asked to testify or release details about subpoenas at City Hall. Testifying before a grand jury is not an admission of wrongdoing, and witnesses are not bound by grand jury secrecy rules.

Walsh’s spokeswoman, Laura Oggeri, said in a statement that “the mayor feels he has an obligation to protect the confidentiality and uphold the integrity of any investigation that may be ongoing.”

Political scientist Paul Watanabe of the University of Massachusetts Boston said that Walsh has generally gotten high marks as mayor. He has been fair advocating for organized labor, Watanabe said, but he has not bent over backward for his core constituency.

But some constituents may lose patience if Walsh continues to leave questions unanswered about the federal investigation, said Watanabe.

“He set the bar pretty high on transparency when he was first elected as mayor,” said Watanabe who served on Walsh’s transition team. “He himself argued that he would be as transparent as possible. In not divulging information such as this, he may not be meeting the standard he himself established.”

City Council President Michelle Wu said people “shouldn’t jump to any conclusions.”

“If there are ongoing investigations, that will play out, but that doesn’t impact our day-to-day work at the council,” Wu said.

The Globe reported Sunday that an investigation into allegations of strong-arm tactics by unions has brought scrutiny to City Hall and to Walsh’s work as a labor leader before taking office in 2014. Walsh became partly drawn into it through wiretaps on which he was recorded in 2012, saying he had told a development company it would face permitting problems on a planned Boston high-rise unless it used union labor at another project in Somerville, according to people familiar with the investigation.

Walsh has said he did not threaten developers. In an interview Saturday, Walsh said he had not been contacted by federal investigators about his time as a union leader.

A member of Walsh’s administration was cited in an indictment last year of five Teamsters members accused of extortion for allegedly harassing a “Top Chef” television production crew that was using nonunion workers. Walsh did not address whether he has been contacted by federal investigators on this issue.

“Prior to running for mayor, Marty Walsh spent a little over two years working for the building trades advocating on behalf of working men and women in and around Boston. He is confident that he always acted ethically and appropriately in that role,” Oggeri said in another statement. “Whatever broad review of labors activities that may be going on, it has little to do with the Walsh administration.”

The US attorney’s office in Boston has a history of prosecuting crimes by local labor unions, including extortion.

In the late 1970s, members of the Teamsters Local 25 were convicted for strong-arming a Hollywood production crew filming the movie “The Brink’s Job.” More recently, three union members of the former Teamsters Local 82, including executive secretary Joseph Perry, were convicted in federal court of extorting jobs from nonunion companies.

Local union leaders continue to defend their right to picket, saying there is a difference between protesting and extortion.

Lawyers for the five Teamsters members accused of bullying the “Top Chef” production crew have filed motions to dismiss the case, saying the type of protests that are alleged – even if they are vulgar – are lawful union activity. The AFL-CIO has intervened and filed its own motion to dismiss the charges.

The outcome of the case, which has not yet been set for trial, could foreshadow how prosecutors and defense attorneys view union activity and the type of strong-arming that has been alleged.

“The courts have traditionally recognized those rights and have endorsed those rights to advocate, to picket, to lobby and bargain and be a force in favor of people’s rights,” said Martin Weinberg, a prominent Boston attorney who has followed the union cases.

Weinberg was not addressing Walsh’s role in the federal investigation, but said there is a difference between the extortion that was prosecuted in the Perry case, and the allegations in the “Top Chef” indictment.

“I think the US attorney’s office is engaged in a difficult challenge to try and determine where the line should be drawn,” Weinberg said.

Jack W. Pirozzolo, a former first assistant US attorney in Boston, said a decision about whether to prosecute any union activity as criminal wrongdoing will be based on a review of the evidence, whether it involves Walsh or anyone else.

Pirozzolo, who left the office in early 2014 and is now a partner with the Boston office of Sidley Austin LLP, was not directly involved in any union investigation, but he said the office in general has invested resources into understanding and investigating union racketeering.

“I think at any level, it’s really going to be driven by the evidence,” Pirozzolo said. “I don’t think they would be looking to bring a case because he’s the mayor, just like I don’t think they’d be looking to not bring a case because he’s the mayor. At the end of the day it will be based on the evidence.”