ALBANY — The state Senate on Wednesday passed a bill that would allow a greater amount of private sector pensions to be exempt from taxes, creating a benefit closer to the tax-free pensions that most retired government workers already enjoy.

The bill sponsored by Sen. Hugh Farley (R-Schenectady) was sent to the Democratic-led Assembly, where similar measures have faced opposition. The measure was discussed, but ultimately dropped from the state budget agreement in April.

Farley has said the tax relief could help slow the exodus of retirees out of state to places like Florida, where pensions aren’t taxed.

Under current law adopted in 1981, the first $20,000 of pension or retirement income is exempt from state income taxes. Farley’s bill would exempt $25,000 from taxes in 2017, $30,000 in 2018, $35,000 in 2019 and $40,000 in 2020 and in following years.

The Senate estimated 377,000 retirees would benefit.

“This tax exemption has never been adjusted and has not kept up with increases in the cost of living,” Farley said Wednesday. “I believe that reducing the tax burden on seniors will help improve their quality of life, encourage them to stay in New York, and provide more equitable treatment of private pensions in comparison to government pensions.”

In New York, tax-free pensions for former government and school workers are protected by the state constitution.