The council passed a unanimous resolution, asking the president to defer the deportations to protect impacted families.
The resolution calls on the president and Congress to support comprehensive immigration reform.
"Sometimes when they detain both parents, these kids are ending up in foster care, and they're separating our families. And the family is the number one thing to the Latino culture," said Tatiana Lopez with the Hermandad Mexicana Humanitarian Foundation.
Critics say nearly two million people have been deported by the Obama administration.
The president has been under growing pressure from immigration rights activists. Last week, the president said immigration policies will be reviewed to see if enforcement can be done in a more humane fashion, within the confines of the law.