LOS ANGELES, May 3 (Reuters) - The FBI said on Thursday it will investigate Los Angeles police officers for possible violation of civil rights when they fired rubber bullets and swung batons at crowds leaving a peaceful pro-immigration rally this week.

The FBI decision will have the backing of city officials. Los Angeles Mayor Antonio Villaraigosa said earlier in the day he would embrace an FBI probe after Police Chief William Bratton said the bureau's involvement might be in order.

In a statement, the FBI said "the results of the FBI's inquiry will be forwarded to the Department of Justice, Civil Rights Division, where a decision whether or not to open a full investigation will be made."

Televised images of Los Angeles police in riot gear showed hundreds of officers pushing and firing at mostly Latino demonstrators and journalists at MacArthur Park on Tuesday in a rare instance of violence since immigrant rights marches began a year ago.

With Los Angeles' history of heavy-handed policing, Bratton moved quickly to open an internal probe and suggested the FBI run a parallel investigation.

"If the chief believes the FBI should be involved I would embrace that," Villaraigosa said in Mexico City.

An internal investigation alone would not be transparent enough to punish police officers deemed to have used unnecessary force, some politicians and rights groups say.

Politicians from outside California also entered the fray.

"With all due respect to chief Bratton, the long history of problems within the LAPD does not inspire confidence in an internal review," New Mexico Gov. Bill Richardson, also a Democratic presidential candidate, said on Thursday, referring to the Los Angeles Police Department.

Los Angeles police have struggled for years to repair their image after the 1991 videotaped beating of black motorist Rodney King by four officers. The men were acquitted in 1992, sparking some of the worst urban riots in modern U.S. history.

Some 25,000 people marched through the streets of Los Angeles on May 1 as part of nationwide protests intended to demonstrate the political might of Latinos and help win amnesty for illegal immigrants.

The rallies come as legislators seek to provide tougher border control and workplace enforcement while addressing the status of illegal immigrants -- an issue Villaraigosa addressed on his tour of Mexico and Central America.

Villaraigosa, who is due to meet Mexican President Felipe Calderon on Friday, urged Mexico to do more to provide jobs and alleviate the poverty that pushes immigrants to search for work in the United States. (Additional reporting by Tim Gaynor in Phoenix and Noel Randewich in Mexico City)

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