(Reuters) - The Detroit City Council on Tuesday unanimously approved the issuance of up to $660 million of refunding bonds to save an estimated $37 million and help pave the city's return to the municipal market after a trip through bankruptcy.

The council also agreed to put aside $30 million from a budget surplus to deal with a possible pension funding shortfall of nearly $500 million.

Mayor Mike Duggan disclosed the potential shortfall earlier this year, warning the city may sue consultants who worked on its bankruptcy exit plan which projected future pension payments using outdated mortality tables. Last week, the city council agreed to hire actuarial consultant Cheiron to work on a new pension funding model.

The plan to refund up to $275 million of unlimited tax general obligation bonds sold in 2014 and up to $385 million of limited tax GO bonds sold in 2010 and 2012 now heads to the Detroit Financial Review Commission for final approval. The city's post-bankruptcy oversight commission meets on June 27.

The bonds, backed by state revenue earmarked for Detroit, would be issued through the Michigan Finance Authority in a deal lead by underwriter Barclays in late July. It would mark Detroit's first GO bond issuance in the market since it exited the biggest-ever U.S. municipal bankruptcy in December 2014.

"We hope this leads to a better general obligation bond rating, which would help us in the future," John Naglick, Detroit's finance director, told the city council.

After defaulting on bond payments just prior to and during its historical bankruptcy that began in 2013, Detroit's GO bond ratings fell deep into "junk" territory and are currently B3 with Moody's Investors Service and B with Standard & Poor's. Ratings in the single-A or double-A level are expected for the refunded bonds due to an intercept mechanism that will send revenue earmarked for debt service payments directly to the bond trustee, according to a report by the city council's legislative policy division.

Detroit plans to take advantage of record-low yields in the muni market to refund the bonds, saving $15 million for the next two city budgets and about $20 million for property tax bills.

In its first post-bankruptcy public debt offering last August, the city restructured $245 million of variable-rate revenue bonds backed by city income taxes into a fixed-rate mode.

(Reporting by Karen Pierog in Chicago; Editing by Matthew Lewis)