LOS ANGELES (AFP) - Over 4,000 people marched in Los Angeles and Arizona for illegal immigrant rights as a senior Catholic church official said the U.S. Congress had a "moral responsibility" to pass laws regularizing the immigrants' status.

Compared to massive marches across the country early this year, only small crowds could be mustered to protest on the eve of a new session of Congress which could consider competing laws that would either give rights to undocumented immigrants or subject them to criminal charges.

"About 3,500 people turned out for a Labor Day Parade in Wilmington (south of downtown Los Angeles), including about 400 people holding a Labor Solidarity March," said Los Angeles police spokeswoman Martha Garcia.

In the Arizona city of Phoenix, close to the border with Mexico where most illegal immigrants cross over from, police said only about 900 joined Monday's protest, which remained peaceful despite a counter-protest by about 100 people carrying signs telling illegal to leave the United States.

Recently hundreds of immigrants turned out in Chicago for a four-day, 50-mile (80-kilometer) trek across the city and its suburbs to press the case for immigration reform and to protest the political gridlock on the issue.

The U.S. Labor Day holiday weekend marches immigrant rallies across the country earlier this year. In Los Angeles a half million people marched for immigrant rights in March and May, and in Phoenix 100,000 people turned out.

Organizers are campaigning for a regularization of the status of an estimated 12 million people who have sneaked into the United States without legal documents, most of them from Latin America.

They hope to pressure Congress to pass proposed laws giving illegal immigrants legal status before the November 7 national elections.

President George W. Bush has called for reforms that would provide for a guest worker program and a path to citizenship for some undocumented migrants.