Miami-Dade Mayor Carlos Gimenez on Tuesday proposed raising the property-tax rate for the first time in three years to stave off cuts to fire and library services and fund a plan to stop killing dogs and cats at the county’s animal shelter.

The mayor’s 2013-14 budget increases the overall tax rate by 5.37 percent, a hike Gimenez said would avoid fire station and public library closures and pay for the animal-welfare plan that nearly 65 percent of Miami-Dade voters approved in a non-binding ballot question in November.

The hike includes the separate portion of taxes that pays for construction projects voters approved in a major bond issue a decade ago, such as expanding the Florida exhibit at Zoo Miami.

In an unincorporated neighborhood such as Kendall, a homeowner with a taxable property value of $200,000 would pay an additional $102.52 in county taxes, which make up only a portion of a total tax bill. The higher fire and library rates would not affect residents of cities with their own fire or library services.

The county had faced a $50.7 million general-fund budget hole, in addition to a $15 million library budget shortfall and a $15 million fire-rescue budget gap. Library and fire services are funded from property taxes separate from the general fund.

To close the general-fund gap, the county froze more than 1,500 vacant positions, used one-time money available from tourist dollars named convention development taxes and relied on higher projections from sales taxes and other revenues. But that did not help plug the fire and library budgets, which had been bolstered the past two years with leftover funds from years prior.

The tax base, which grew 3.39 percent thanks to climbing property values, did not expand as much as the county had hoped, Gimenez said, and Florida lawmakers imposed higher, unforeseen Medicaid and Florida Retirement System obligations that resulted in nearly $30 million in additional expenses.

The mayor’s short-lived plan to shutter 13 libraries two years ago received so much pushback from county commissioners who must ultimately set the tax rate and approve the budget that the mayor this time decided to suggest a tax-rate hike instead.

“I don’t believe the people of Miami-Dade County want to cut back on library services or fire services,” Gimenez said, noting that he expects his proposal to sustain the county for two years.

But while the higher tax rate would protect libraries and fire stations, it still could pose a political dilemma for commissioners, and will do nothing to stem conflict with the county’s labor unions over concessions that had been scheduled to expire next year.

Gimenez’s budget calls for workers to continue contributing 5 percent of their base pay toward health insurance costs and for extending other concessions. The county would otherwise have to cut about $37 million from the general fund.

Most three-year union contracts provide for reopening certain provisions if the healthcare contribution is to continue past Jan. 1, 2014. The firefighters union is exempt because it has its own insurance.

Union chiefs have accused the county of carrying an unnecessary $42 million surplus in its health-insurance trust fund, which the administration counters helps maintain benefits and hold the line against health-insurance rate increases in the future. Miami-Dade Clerk of Courts Harvey Ruvin has agreed to conduct a financial audit of the fund at the unions’ request.