SPRINGFIELD, Ill. (Reuters) - A bill to restructure Chicago's payments to its public safety workers' retirement funds by lowering contributions in the near term won final legislative approval on Sunday from the Illinois Senate.

The 38-20 vote on the last day of the Democrat-controlled legislature's spring session will send the measure to Republican Governor Bruce Rauner.

But it was unclear if the Republican governor will sign the measure into law. In an unprecedented speech to the Chicago City Council on May 6, Rauner said: "For Chicago to get what it wants, Illinois must get what it needs."

And Rauner's lengthy agenda of "needs" has so far been snubbed by Democrats whose members outnumber Republicans 39 to 20 in the Senate and 71 to 47 in the House.

Representatives for Rauner did not immediately respond to a request for comment on the bill.

Under a 2010 state law, the city's contribution to its police and fire fighter funds next year increases by $550 million to about $839 million. The bill would reduce that amount by about $220 million, to $619 million. Chicago's payments would increase every year between 2017 and 2020, but not as much as under the 2010 law.

After 2020, the city's contributions would be calculated at amounts that would enable the two pension systems to become 90 percent funded by 2055, which is 15 years longer than in the 2010 law.

Chicago's finances have been squeezed by a $20 billion unfunded liability in its four pension funds and by a credit rating downgrade to junk earlier this month by Moody's Investors Service that triggered $2.2 billion in accelerated debt payments and fees.

Republicans criticized the bill for letting Chicago off the hook for the larger payments the city has been aware of for years and for promising benefits to its workers it could not afford.

"This is nothing more than a pension holiday, and when you're down to 25 percent funded, that's no vacation. This is serious and they need to start taking it seriously in Chicago," said state Senator Matt Murphy, a Republican from Chicago's suburbs.

Democrats said the bill, pushed by Chicago Mayor Rahm Emanuel, was aimed at smoothing out the city's pension contributions and avoiding a big property tax increase on city residents.

If Chicago fails to make required pension payments, the bill allows for an intercept of state funds due the city and for the retirement funds to go to court to force payments.

The bill also requires proceeds from a Chicago casino in the future to be allocated to the public safety retirement funds. Emanuel has been asking state lawmakers for a bill authorizing a city-owned casino, but that legislation did not advance.

(Reporting by Karl Plume in Springfield; Editing by Sandra Maler and Eric Walsh)