The city leaders sent the letter as Congress is weighing cuts to the Supplemental Nutrition Assistance Program, the formal name for food stamps.
Nutter has twice tried and failed to enact a tax on sugar-sweetened beverages in Philadelphia, and has been outspoken about the issue.
The office of New York City Mayor Michael Bloomberg released the mayors' letter. Bloomberg has received national attention for trying to ban sales of large-size sugary drinks and has previously tried to prevent food stamps from being used for soda.