In the letter he urged the U.S. House to address immigration reform "as soon as possible."
The Senate passed a bill in June that would put the estimated 11 million undocumented immigrants living in the U.S. on a path to citizenship, but Boehner has resisted calls to bring it to a vote.
Writing on behalf of the 450-plus U.S. cardinals and bishops Cardinal Dolan said “keeping undocumented immigrants "as a permanent underclass of workers who are unable to assert their rights or enjoy the fruits of their labor is a stain on the soul of the nation."
As pastors, we witness each day the human consequences of a broken immigration system," he said. "Families are separated through deportation, migrant workers are exploited in the workplace, and migrants die in the desert.
"In their attempts to respond to these human tragedies, our priests, religious, and social service providers in many cases are unable to help these persons without changes to the law," the cardinal added.
In his letter, Dolan reiterated the Catholic bishops' call for reforms including: creating "a fair and achievable path" to citizenship for the country's 11 million undocumented immigrants; permitting future migrant workers to enter the U.S. safely, legally "and with appropriate protections."
"Immigration reform would protect that right and restore the rule of law while upholding the human rights and dignity of the person," he continued. "As a moral matter, however, our nation cannot continue to receive the benefits of the work and contributions of undocumented immigrants without extending to them the protection of the law."
President Barack Obama has made immigration reform one of his top priorities for the rest of the year.
Responding to Dolan's letter, Michael Steel, a spokesman for Boehner, said the speaker "has been very clear that he supports common-sense, step-by-step reforms to fix our broken immigration system."