A trust fund that pays medical bills for Chrysler blue-collar retirees has asked the company to set up a public sale of Chrysler stock.

The United Auto Workers trust, which owns 41.5 percent of Chrysler's shares, on Wednesday asked Chrysler to start the process for an initial public stock offering. The trust wants the company to sell 16.6 percent of the stock owned by the trust, Chrysler said.

Italian carmaker Fiat SpA, which owns the remaining 58.5 percent of Chrysler, is fighting the trust in a Delaware court over the value of Chrysler shares. Fiat has options to buy up to 16.6 percent of the trust's shares. It has filed plans to buy 6.6 percent and says it wants to buy the rest.

Fiat and the trust got their shares after the U.S. government bailed out Chrysler in 2009.

The request for Chrysler to file paperwork with the U.S. Securities and Exchange Commission is the first step toward a public sale that could take many months.

Chrysler and Fiat said in statements that they will comply with obligations of the Chrysler ownership agreement, but neither committed to a public stock sale. The trust fund and the UAW declined comment.

Fiat has made offers to the trust to raise its stake to 65.17 percent in two tranches. But the sales have been held up by the court fight.

Fiat said that the offer for the second tranche of 3.3 percent made earlier this month is worth $198 million, but the trust wants more money.

Sergio Marchionne, who is CEO of both Fiat and Chrysler, has said that Fiat's planned investment in Italy to boost production means the company does not have the cash to buy the trust's shares outright.