By Alex Dobuzinskis

LOS ANGELES (Reuters) - U.S. authorities have agreed to stop pressuring undocumented immigrants in Southern California to sign off on their own deportations under a legal settlement that may later allow some deportees to return from Mexico to seek U.S. legal residency, advocacy groups said on Wednesday.

The deal reached between the American Civil Liberties Union and federal officials stems from a lawsuit brought last year on behalf of other immigration rights groups and about 10 immigrants who accepted so-called "voluntary returns" to Mexico.

All of the immigrants had strong grounds for being allowed to remain in the United States after entering illegally because of family ties and a lack of criminal history, and they will now be permitted to present their claims in U.S. immigration court, ACLU attorneys said.

The settlement is limited in scope as most of reforms agreed to by U.S. immigration officials apply only in Southern California, where the ACLU documented what it said were deceptive and coercive practices dating back to 2009.

The reforms include allowing undocumented immigrants access to a telephone and two hours to reach a legal adviser before deciding whether to sign a voluntary return form waiving their rights to seek a hearing to challenge their deportation.

Federal authorities also agreed to ensure immigrants are informed that once they are deported they would be barred from legal re-entry for 10 years, ACLU attorneys said.

Moreover, the deal paves the way for a federal judge in Los Angeles in the coming months to potentially allow for some Mexican migrants already deported under the process in question to return for immigration hearings, said Gabriela Rivera, staff attorney with the ACLU of San Diego.

Such a ruling depends on the judge first certifying that all such immigrants deported since 2009 constitute a legal class under the settlement.

Hundreds of thousands were sent back to Mexico through voluntary returns from California, but anyone in that group seeking to re-enter the United States under the settlement would need to apply based on a set of criteria defining the class.

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Those criteria cover such situations as having lived in the United States for 10 years and having a U.S. citizen child who would suffer hardship through separation, or having a spouse or parent who is a U.S. citizen, Rivera said.

"People who were tricked or misled into signing these forms are now finally going to have their day in court before an immigration judge, which they were denied when they signed these forms in a really unfair and unknowing way,” Rivera said.

Marsha Catron, a spokeswoman for the Department of Homeland Security, said immigration officials do not tolerate "coercion or deception" in the voluntary return program.

"In an effort to address the issues raised in this litigation ... agencies have agreed to supplement their existing procedures to ensure that foreign nationals fully comprehend the potential consequences of returning voluntarily to Mexico," she said.

(Reporting by Alex Dobuzinskis; Editing by Steve Gorman and Eric Walsh)