Hundreds of fans turned out to greet the actors and costar Kate Winslet at Tulane University.
On the red carpet, Law said, "The city welcomed us with such open arms and after Katrina, it was even more important that we come here."
Director Steven Zaillian was proud to be back in New Orleans: "It's something everyone wanted to do. It just seemed right."
Louisiana Governor Kathleen Blanco used the film's premiere to personally thank Penn for his personal efforts in the days following the storms.
Penn was among the first celebrities to visit the devastated region and helped volunteers and rescue workers seek out survivors, clean up the damage and find refuge for the homeless.
The movie star received a standing ovation after Blanco made her comments known.
Another preview screening of the film is scheduled for Tuesday in Baton Rouge, Louisiana, where part of the movie was filmed.
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