The program is called Secure Communities, and under it, the fingerprints of anyone arrested are sent to federal immigration authorities.
If a detained person is undocumented, they can be deported based on the severity of the crime they are alleged to have committed. Members of the immigrant rights group Casa De Maryland held a press conference outside the council building in Rockville Tuesday.
Gustavo Torres, the group's executive director, says the program has led to people being deported even though they were not convicted of a crime.
That has led to many people not cooperating with police out of fear of deportation, he adds.
"President Obama, Mr. President, please take out this program, because it is not helping our community at all," says Torres. "By the contrary, it is creating fear in our community, and we really need you to stop this."
Last week, members of the Montgomery County Council pushed a resolution that called for the county police not to take part in the program. But they backed off after learning that the federal government has stated that the activation date for Secure Communities in the county is in September.
They instead passed a measure stating the program should focus only on deporting those actually convicted of serious crimes.