The Church of Latter-Day Saints’ Cambridge Stake Center is nearing completion near Kendall Square, but with nonunion labor contrary to an agreement made by Consigli Construction Co., officials say. (Image: Consigli Construction Co.)

The builders behind Cambridge’s Main Library, City Hall and high school renovations were called liars Monday by City Council members angry over the company’s failure to follow through on labor promises.

The failure of Consigli Construction Co. to provide pledged apprenticeships to city youth was a top concern, but not the only one. “Consigli is a company that has failed repeatedly to make good on its word,” councillor Marjorie Decker said in bringing forward a late order at a Monday meeting. “I have a number of concerns in terms of their work ethic and truthfulness.”

The Milford-based construction company is to wrap up work this month on a 35,892-square-foot structure for the Church of Latter-Day Saints at Binney, Rogers and Second streets. But the site is being picketed daily by workers from the International Union of Painters and Allied Trades who share Decker’s anger over wages, benefits and apprenticeships Consigli is providing as contractor, as well as its use of nonunion contractors to finish the project.

“This is not in itself a large job, but it’s important because commitments were made. When a developer says we’ve made a commitment and it’s broken and that’s not addressed, it opens a door” to future abuse, said John S. Laughlin, director of political and public relations for the Boston union.

The church has reached out to union workers and seems blameless in how Consigli is building its Cambridge Stake Center, according to Laughlin and councillors.

Consigli principals, however, drew repeated fire as liars for denying they made labor commitments. Several councillors spoke to confirm Consigli’s promises as described by Decker. Councillor David Maher was among those recalling that the Stake Center was to be “100 percent a union job. That may have been the intent of the developer, but that’s not what happened.”

“I too recollect meeting last term,” councillor Sam Seidel said. “There was no way we would walk out of that room without an agreement. All interested parties were there … that was my very strong recollection.”

It would be one thing for Consigli officials to say they had changed their minds, Decker said, but instead they merely deny assuring work would be done by union members or that there would be more than two apprenticeships for local youth. For many who choose not to go to college, Decker said, apprenticeships have long been a path to good wages and a dignified life.

“For them to tell me these meetings never took place is a lie,” Decker said. “To say it never happened, when several of us were part of that conversation — and there’s a public record of the church coming to the council and acknowledging this!”

Craig Kelley opposes late orders in general, and spoke of feeling conflicted over this one — sharing dismay over the allegations against Consigli but wishing the issue had been brought to the council in a more orderly way so the company could have representatives on hand to answer them. Because the issue is urgent but brought to her attention only Friday, waiting a week to bring the order forward was impossible, Decker explained. But she said she spoke with Consigli officials over the weekend and gave them ample warning the company would be discussed.

Consigli officials chose not to appear, she said.

Consigli also chose not to reply Monday night or Tuesday to e-mail and telephone messages left with them asking for comment about the council complaints.

An impassioned Decker made a formal request for City Manager Robert W. Healy to look into the situation and report back. Councillor Ken Reeves noted that Consigli is still working on the renovation of Cambridge Rindge & Latin School, and that could give the city leverage in holding the company to its promises.

The revamped school is due to open in September. Consigli is working alongside JJ Construction on the two-year project, for which the city’s budget office has given a price tag of $112 million, a savings from preconstruction estimates of $125 million.

Consigli was founded in 1905 and has about 330 employees, 134 of which are listed as working in Massachusetts. It listed revenue in 2008 at $315 million.

During its overlapping work on the library and high school, Consigli won a blurb from Rossi that is posted on its Web site: “Consigli Construction has shown professionalism throughout the entire project. Their dedication, flexibility and processes set them apart from others that have worked with the city. We would welcome the opportunity to work with them again in the future.”