SAN DIEGO — Far fewer immigrants arrested in California are being turned over to federal authorities for deportation since a new state law went into effect in January.

The law was pushed by immigrant advocates and directs law enforcement agencies to more quickly release those without serious criminal records rather than hold them so federal officials can take them into custody for deportation proceedings.

Already, according to a review by The Associated Press, the new law appears to be having a big impact in slowing deportations at a time when President Obama is looking to ease immigration enforcement policies nationwide and appease immigrant advocates who say his administration has been too tough.

Until now, California has accounted for a third of deportations under U.S. Immigration and Custom Enforcement’s Secure Communities program, which screens the fingerprints of arrestees for potential immigration violations.

It was expected the state law known as the Trust Act would reduce the number of people held for possible deportation, but wasn’t clear how significant the drop would be.

Since sheriff’s departments are responsible for most bookings, the AP surveyed those agencies in 23 counties. Not all supplied data for the first two months of 2014, but among those that did, there was a 44 percent drop, from 2,984 people to 1,660.