MEXICO CITY, May 4 (Reuters) - Los Angeles Mayor Antonio Villaraigosa has cut short a trip to Mexico to deal with a growing scandal over a clash between police and pro-immigration protesters in the city earlier this week.

Villaraigosa arrived in Mexico City on Thursday for a six-day visit to discuss issues like immigration, but will now fly home on Friday. He met President Felipe Calderon on Thursday but canceled a Friday meeting with Mexico City Mayor Marcelo Ebrard and visits to other Mexican cities.

"It's time to go back; they want me to be there," he told a news conference. "We all know ... this is a serious matter."

Villaraigosa said on Thursday he would welcome an FBI probe of Los Angeles police officers for possible civil rights violations after they fired rubber bullets and swung batons at crowds leaving a generally peaceful pro-immigration rally.

Televised images of police in riot gear showed hundreds of officers pushing and firing at mostly Latino demonstrators and journalists at MacArthur Park on Tuesday. Local media reported that a number of people were injured, including news reporters.

The Los Angeles Police Department has a history of heavy-handed policing. It has struggled for years to repair its image after a videotaped beating in 1991 of black motorist Rodney King by four officers.

Some 25,000 people marched through 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.

Villaraigosa, a former Latino activist turned politician, wants U.S. immigration reforms rather than a partial border fence backed by Congress. "We should build bridges, not walls," he said.

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