By Fiona Ortiz and Karen Pierog

CHICAGO (Reuters) - Illinois Governor Bruce Rauner told the Chicago City Council on Wednesday that the state's "terrible financial crisis" means there is no money to bail out the city from its own fiscal mess.

The governor, in an unprecedented address to the Democratic council, said the city and state need to work together to address problems that include big unfunded pension liabilities facing both governments.

Rauner has been touring the state to sell his "turnaround" agenda that includes cuts to public pensions and controversial proposals like creating local right-to-work zones where union membership would be voluntary instead of mandatory.

Ahead of his speech, Chicago aldermen adopted a resolution against that proposal.

Though Rauner is a Republican and Chicago Mayor Rahm Emanuel a Democrat, the two have been close friends and even political allies in the past, and they share an agenda of strengthening government finances.

Emanuel, re-elected in April, faces growing deficits in the city and school budgets.

Rauner and Emanuel both said on Wednesday that the city and the state must make sacrifices to reach a joint solution, but neither provided much detail of where compromise may be found. Illinois has the lowest credit rating of any U.S. state, which makes it expensive to borrow money.

"For Chicago to get what it wants, Illinois must get what it needs," Rauner said to a city council chamber packed with union members.

"It's not easy," he told reporters, who asked him where he was willing to give, after his 8-minute speech to the city council.

The governor was not receptive to Emanuel's pet tax reform proposal aimed at ending Chicago taxpayer funding of both the Chicago Public Schools' teacher pensions and those of school districts outside of the city. Rauner said Chicago schools receive a disproportionate amount of funds relative to other school districts in the state.

Rauner also told reporters he accepted the city council's rejection of his turnaround agenda. He said his plan is to encourage local Illinois governments to decide on the issue themselves.

"That's my point ... local communities should be empowered to decide how their economies compete," the governor said.

Rauner's proposed fiscal 2016 Illinois budget would cut state funding for Chicago by about $135 million as part of a plan to fill a gap of more than $6 billion.

(Editing by Grant McCool and Matthew Lewis)