Under terms of the agreement, Fiat has the option to abandon the deal if it is not completed by June 15.
"Fiat won't walk away from Chrysler," Fiat spokesman Gualberto Ranieri said.
The U.S. Supreme Court decision on Monday to hear a challenge by three Indiana pension and construction funds could ultimately scuttle the sale. But the delay could also only be temporary. Justice Ruth Ginsburg could decide on her own to end the stay or ask the full court to decide.
If Fiat were to walk away, Chrysler would have little option but to liquidate.
The trio of funds, which hold a small part of Chrysler's debt, have been fighting the sale, claiming that it unfairly favors Chrysler's unsecured stakeholders ahead of secured debtholders like themselves.
Chrysler claims the agreement with Fiat is the best deal it can get for its assets and is critical to the company's plan to emerge from bankruptcy protection.
Fiat has offered its small car and environmentally friendly engine technology, as well as management expertise, in exchange for an initial 20 percent stake in Chrysler, which will grow to 35 percent in 5 percent increments. Fiat CEO Sergio Marchionne, who was in Detroit on Tuesday laying the groundwork for the transition, will also become Chrysler's chief executive when the deal is complete.
Marchionne, who is responsible for Fiat's turnaround from a loss-making company with a string of failed models, also is expected to bring fundamental changes to the Chrysler management structure — doing away with hierarchy and making a quicker decision-making process.
Marchionne also remains interested in Germany's Opel, part of General Motors Corp.'s European operations, in case negotiations fail with the leading bidder, Canadian auto parts supplier Magna International Inc.