Wakefield Council leader Peter Box has claimed the authority's deal with a private company working in 86 local schools is "good value for money".
ENGIE was handed a bumper contract in 2016 to take on a number of council services, including building projects and property maintenance, in what was the biggest privatisation in the local authority's history.
It was meant to save taxpayers £10m over a decade, but the arrangement came under scrutiny in September when the council said ENGIE had failed to meet 900 specific obligations.
The company was fined for this and it was suggested the partnership may be ended early if things didn't improve.
The authority then said that the exact value of the deal so far would not be known until March.
But at a meeting of full council on Wednesday, Coun Box appeared to suggest that the promised savings were being delivered.
Asked about the issue by opposition leader Nadeem Ahmed, Coun Box said: "To date, we've received over £3m from the partnership in savings over the first two years.
"A value test on capital construction work has been carried out, showing we get good value for money.
"We're currently reviewing the rates we pay for work, which is showing further savings may be achievable."
The Labour leader added that the deal was constantly "under review" to ensure it delivered on what was promised.
As part of its obligations, ENGIE also delivers catering and cleaning services in schools.
A total of 734 council staff had their contracts transferred to the company after the deal was brokered.