However, Chrysler and White House officials argued the move to block the deal could cause the entire deal to collapse, causing "grave consequences."
Chrysler filed for bankruptcy protection in April and had planned to complete the sale to Fiat within 60 days.
It is not clear how long the judges will take in their review of the sale but the administration of Barack Obama has set a deadline of June 15, as Fiat says it will walk away if the deal is not completed by then.
The Indiana pension funds argued that the sale of Chrysler unlawfully rewards unsecured creditors ahead of secured lenders and amounts to an illegal reorganisation plan.
They also say the US Treasury Department overstepped its legal authority by using some of the $700bn bailout funds from the Troubled Asset Relief Program (Tarp) to finance Chrysler's restructuring when US congress had intended the money to be used for only for ailing US banks.
A US government brief countered that "the only other alternative is the immediate liquidation of the company" which would be detrimental to all Chrysler's creditors.
The move could also have repercussions for US auto firm General Motors (GM), which also entered bankruptcy protection on June 1 and is using a similar quick-sale strategy in its bankruptcy in New York.
A US judge in New York, in an order approving the Chrysler restructuring on May 31, agreed to allow the planned tie-up with Fiat to be completed rapidly.
Judge Arthur Gonzalez said he agreed to the accelerated plan after the White House auto task force argued that the automaker was losing $100m for each day the plan was delayed.
The current plan gives Fiat a 20 per cent stake in the Detroit-based firm group, with
a possibility of increasing this stake in the future.
In return, Fiat will allow access to its technology to enable the US carmaker to make the smaller, greener cars that are increasingly in demand.
The new firm would be mostly owned by the United Auto Workers (UAW) union, with small stakes by the US and Canadian governments, which would contribute about $10.5bn.
US carmakers were hit hard by the current US recession and were criticised for failing to develop more fuel efficient vehicles as demanded by the consumer.