For the third consecutive year, Oakland is boosting its contribution of public money to a nonprofit contractor whose chief executive officer has repeatedly blamed the city for the organization’s financial distress.

The Oakland Private Industry Council holds a $1 million annual city contract to provide job training and placement services, largely through a downtown career center on Broadway. CEO Gay Plair Cobb has fought for the extra funding, helping the Private Industry Council collect an additional $250,000 in public funds last year after threatening to stop services, and an extra $50,000 in 2014.

This year, the city is on track to hand the Private Industry Council an extra $275,000. Some of the money would come from federal and state funds designated for job services and training. Some would come from the city’s general fund, which also pays for such basic services as police, firefighting, libraries and public works.

The group’s repeated requests for public funds have caused dissension in City Hall. While several council members have thrown their support behind the Private Industry Council, other officials say the city should insist on tighter financial controls.

The Private Industry Council “needs to manage its own budget,” Oakland’s economic development chief, Mark Sawicki, said in an interview. “When there are shrinking dollars available, organizations need to either downsize or go after money from other sources. And there are other sources available — not just the city.”

Yet, on Nov. 3, Oakland’s Workforce Development Board, a city authority that doles out federal and state funds for job programs, voted to award the group an extra $65,000 at Cobb’s behest — an award that is pending approval from the City Council in December. And on Tuesday, the City Council will vote on whether to give the group $150,000 from the general fund to stave off a lawsuit threat from Cobb, who says the city owes the money as a penalty for late payments in previous years.

Additionally, Cobb and the other Private Industry Council staffers are asking the City Council for $60,000 in general fund dollars to bolster a neighborhood job center in West Oakland.

“We’re tired of coming back time after time after time to this body, literally begging for resources,” Cobb told a committee of the City Council at an Oct. 25 meeting.

In an Oct. 28 email responding to questions raised by The Chronicle, Cobb accused the city of being incompetent and said its “missteps” represent “undue denial and delay of services to the people who need them most.”

Part of the $65,000 that Cobb requested from the Workforce Development Board was to compensate her organization for services it performed without the city’s authorization. The group argued it should be paid $18,000 for job services it offered to laid-off employees of three companies — ConAgra Foods Inc., ITT Technical Services Inc. and IAC Search & Media Inc. The companies laid off a total of 84 workers over the summer.

The Private Industry Council would use the rest of the $65,000 on future assistance to laid-off workers. The Workforce Development Board agreed on Nov. 3 to amend the Private Industry Council’s contract to retroactively authorize the group’s summer work and to authorize future layoff services through June 2017.

A policy expert said the city’s moves are extraordinary, particularly its contract amendment, which is pending City Council approval.

“People can’t just go out and mow the lawns of city parks and then come back and send a bill to the city,” said Mark Morodomi, who served as Oakland’s supervising deputy city attorney for 12 years, until 2013.

At the Oct. 25 meeting of the council committee, Sawicki noted that the group was asking to be paid for work “apparently beyond what was in the scope of their contract.”

Sawicki also pointed out that of the three companies that shut their doors, two had closed before the city learned about the layoffs.

“That didn’t stop us,” said Richard de Jauregui, the Private Industry Council’s director of planning, performance and program oversight. He said his group had dispatched staff members to each business. They found the doors locked at one of the businesses, ITT, but they left flyers and information packets, he said.

The Private Industry Council has long worked with the city to provide job-training programs that are largely paid for with federal money. From 2001 to 2011, the city entrusted the group with a huge responsibility: overseeing the millions of dollars Oakland received each year in federal job grants. The group awarded grants not just to other organizations, but to itself, a practice that drew concern from the state’s Employment Development Department, which helps administer the federal job funds.

In 2010, a state auditor said the Private Industry Council improperly accounted for or misspent $830,000 in federal stimulus dollars. The audit also found that the group had given job-training money to groups that spent it on such things as church repairs, car allowances and field trips to the Santa Cruz Beach Boardwalk.

In 2011, the city began handing out the federal dollars itself, with the Private Industry Council winning one of several contracts. Two years later the Employment Development Department conducted another audit and found that the city was now properly monitoring its workforce contractors.

Yet Cobb and her supporters have repeatedly slammed the city’s performance. The Private Industry Council has strong support from pastors, community activists and the Oakland Post newspaper, a weekly published by Cobb’s husband, Paul Cobb.

Recently the Post ran a series of articles criticizing the city’s handling of workforce funds. Some articles suggested Mayor Libby Schaaf was trying to shut down neighborhood job centers — an assertion the mayor denied during her State of the City speech in October.

Gay Plair Cobb chided the city at the Oct. 25 council committee meeting, saying officials have cut funding and delayed payments to nonprofit service providers, and passed up opportunities to get federal and state grants.

“In the real world, it is stunning that there is no accountability, nobody loses a job, nobody loses a paycheck,” Cobb told the council members. “The only ones losing a paycheck are the ones delivering the services.”

Council members Larry Reid and Rebecca Kaplan supported Cobb’s request for the extra $60,000 from the city’s general fund. The third committee member present that day, Councilwoman Annie Campbell Washington, raised questions about where the money would come from.

“It’s not clear why they need an additional allocation,” Campbell Washington said later.

Reid accused city officials of deliberately denying the Private Industry Council enough money to keep its doors open, and he added that Cobb has had to pay rent from her own pocket.

“I have an institution that is providing services to those that are less fortunate than us in the room, and they’re struggling to pay their rent,” Reid said. “I’m almost to the point where (I think) we’re doing this on purpose.”

Kaplan directed city staff to find a source for the $60,000 in funding.

At the time of the meeting Kaplan and Reid were running for re-election, and the day after the committee meeting, the Oakland Post endorsed them. They both won.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan