The resolution comes as many in the Latino community are criticizing the president for not taking firmer action against the issue.
"We have to continue raising our voices, tell Congress and America that we will not give up," said L.A. City Council member Jose Huizar.
The news conference held outside of L.A. City Hall Wednesday was sponsored by L.A. Council members Curren Price and Gil Cedillo.
"Deportations have torn up thousands of families right here in our city and it's time that we stop that," said Price.
Immigrant rights organizations say the U.S. is deporting people at a faster rate than anytime in modern history.
According to the Department of Homeland Security, more than 204,000 non-criminals were deported in 2011. That's compared to 92,000 non-criminals who were deported in 2002 under then President George W. Bush.
"I'm very disappointed," said Cedillo.
He says he supported Obama's presidential campaign because he thought Obama would be more sympathetic toward the immigrant community.
"I find it unfortunate that the president has broken a record as being the president that's deported more immigrants than any president in the history of this nation," said Cedillo.
In recent interviews, President Obama has said it would be difficult to halt the deportation of illegal immigrants without the approval of Congress.
But Wednesday's resolution calls on the president to use an executive order, similar to the one he issued last year allowing children who were brought into the country illegally a chance to stay while applying for citizenship.
"I respect the legislative process, but when it's not working, we need executive action and executive leadership," said Cedillo.
There was no immediate response from the White House, but Cedillo says he's certain that President Obama will take note of Wednesday's resolution.