BOSTON — The state’s cities and towns have shed more than 15,000 jobs in the past six years, and pension obligations, health care and borrowing costs will continue to squeeze budgets for the foreseeable future, according to a report issued on Tuesday.

Municipalities face a total of nearly $45 billion in unfunded liabilities, according to The Massachusetts Taxpayers Foundation, an independent, business-backed organization. Meeting those responsibilities could divert resources from schools, public safety and other services, the group warned.