DETROIT – The city of Detroit reached an agreement on Tuesday with two banks to end a costly interest-rate swap agreement, a significant step as the city negotiates with creditors to put together a plan to exit the largest municipal bankruptcy in U.S. history.

Detroit will pay $165 million, plus up to $4.2 million in costs, to end the interest-rate swap agreements with UBS and Bank of America Corp’s (BAC.N) Merrill Lynch Capital Services at a 43 percent discount. The new agreement, which was reached after the judge overseeing the case implored the city to negotiate better terms than it first proposed, will save the city about $65 million.

As part of the arrangement, Detroit will also take out a $285 million loan from Barclays PLC to pay to end the swaps. It will use $120 million of that toward improvements to services in the city, which is hampered by $18.5 billion in debt.

Terms of the agreement were announced by Robert Hertzberg, of the law firm Pepper Hamilton, which represents Detroit, before U.S. District Judge Gerald Rosen, the chief mediator in the bankruptcy case. The deal must still be approved by the U.S. bankruptcy judge overseeing the case, Steven Rhodes.

Robert Gordon, an attorney representing the city’s two pension funds, said the funds would continue to oppose the deal even with the changes. “The revised deal is better, but that is not saying a lot,” Gordon, of the law firm Clark Hill, wrote in an email.

The deal was reached after two days of mediation this week, led by Rosen.

“This is – I think it’s the first, I think it’s fair to say, significant agreement in the bankruptcy,” Rosen said, according to a court transcript.

Detroit had initially secured a $350 million loan from Barclays, of which about $230 million would be used to end the swap agreements with UBS and Merrill Lynch at 75 cents on the dollar. The remainder of the cash was slated to be used to improve city services.

The swaps had been intended to hedge interest rate risk for a portion of $1.4 billion of pension debt Detroit sold in 2005 and 2006.

A spokesman for Bank of America declined to comment. UBS could not be reached immediately for comment.

Rhodes last week encouraged Detroit to negotiate better terms with the banks after he halted a hearing at which the city was seeking approval of the deal.

The agreement can be terminated if it is not approved by January 31, 2014. Detroit plans to file a request with Rhodes to approve the deal by Friday, said Hertzberg, the city’s attorney.

Detroit Emergency Manager Kevyn Orr, in a statement, called the deal an “important development. This agreement represents a significant reduction from the original deal struck with the banks,” Orr said. “The banks and the City, through mediation, and with the mediator’s recommendation, have accepted the reduction in terms.”