Animosity has begun to brew between Gov. Charlie Baker’s administration and public employee unions negotiating new contracts with the state who believe the governor’s team has been low-balling the workers with salary offers that fail to keep up with rising health care costs and increased demands.

Baker is moving into the final months of his third year in office and the likely start of a re-election campaign with a raft of unsettled contracts hanging over his head.

Of the 10 contracts covering more than 35,000 state employees that fall under his purview, five have expired, two extend into the summer of 2018 and three contracts for state police, nurses and firefighters expire at the end of the year.

Several of the largest public employee unions in the state wrote a letter to Baker last Thursday expressing “deep disappointment” in the administration’s bargaining position to date, suggesting that the governor’s office has drawn a line in the sand and won’t accept any collective bargaining agreement that exceeds 5 percent in incremental costs over three years.

“We don’t have unrealistic expectations. We didn’t expect that staffing levels were going to go up under your administration. We didn’t expect that our health care costs would go down. What we did expect however is that we would get a fair shake from you when it came time to negotiate wages. The simple fact is that we haven’t,” the union leaders wrote.

The letter was signed by the heads of the National Association of Government Employees, SEUI Local 509, the Massachusetts Nurses Association, OPEIU Local 6, SEIU Local 888, AFSCME Council 93 and the Massachusetts Teachers Association.

The unions claim that while the cost of living is increasing roughly 2.5 percent a year, the state workers have been offered two raises in fiscal 2018 of just 0.5 percent each. They further suggest that municipal union workers have signed multiyear agreements with cities and towns with increases in excess of 2 percent each year.

“We don’t expect to be treated better than other public employees, but we didn’t expect to be treated worse,” they wrote.

The Baker administration responded to the letter by pointing out ways in which it has worked with unions, including SEIU Local 509, to reduce caseloads on social workers and invest in the Department of Children and Families to improve conditions for workers. The governor’s office pointed to $114 million invested in DCF that has resulted in new hires and progress toward achieving collectively bargained caseload ratios for social workers of 18 to 1.

“The Executive Office for Administration and Finance and the Office of Employee Relations are in ongoing discussions with state employee unions regarding new contracts, and are committed to providing fair and reasonable benefits to our hardworking state employees to continue progress on issues like staffing and caseload management at agencies such as the Department of Children and Families,” Administration and Finance spokeswoman Sarah Finlaw said in a statement.

The letter, according to a spokesman for SEIU Local 509, was hand-delivered to Baker’s office last Friday, around the same time that unions had another bargaining session during which the salary offers from the administration did not change. The SEIU Local 509 represents two bargaining units of 8,439 social workers and secondary education employees whose contract expired on Dec. 31, 2016. The previous three-year contract for those units included 3 percent annualized salary increases for 2014, 2015, and 2016.

In addition to the social workers and school employees, 9,669 clerical, skilled trades and administrative employees unionized by NAGE and 7,918 institutional services employees and 67 corrections officers and 1,725 scientists and engineers are working without contracts.

The unions, who negotiate separately but were aiming to present a unified front, said in the letter that their members have taken “deep cuts in take-home pay” due to increases in health insurance co-pays and deductibles implemented through the Group Insurance Commission by the Baker administration. They have also dealt with budget cuts and staff turnover and reductions because of early retirement programs implemented by the governor to generate budget savings.

“We ask that you reconsider the economic parameters of our negotiations. We ask that you authorize settlements that are more in tune with the increase in the Consumer Price Index, as well as other public sector settlements reached in FY 18 in Massachusetts,” the unions wrote.