Puerto Rico’s default on most of a $422 million debt payment on Monday puts the spotlight back on Washington to enact a rescue package for the island, and congressional aides said a revised bill would be introduced next week.

On Monday, Treasury Secretary Jacob J. Lew renewed his call on Congress to act swiftly, warning in a letter to House Speaker Paul Ryan that without a legal framework for a debt restructuring, Puerto Rico is in danger of getting caught in “a series of cascading defaults” that could lead to a taxpayer bailout.

“This is not just a matter of financial liabilities and litigation,” Mr. Lew said in the letter, which was circulated to other lawmakers and released publicly. Late last year, Mr. Ryan instructed the relevant House committees to find a “reasonable solution” for Puerto Rico.

Mr. Lew, in Monday’s letter and in an interview last month with the Spanish-language television station Univision, cited signs of mounting woes, including the closing of hospital facilities on the island and the struggle to contain the spread of the Zika virus with scant financial resources available. “The human costs for the 3.5 million Americans in Puerto Rico are real. And they are escalating daily,” Mr. Lew wrote.