San Francisco police officers and sheriff’s deputies will not follow President Trump’s executive orders on immigration and arrest residents living in the city without proper documentation, Mayor Ed Lee, Police Chief William Scott and Sheriff Vicki Hennessy wrote in a letter to the Department of Homeland Security on Monday.

Holding strong to their commitment to stand against Trump in his crackdown on immigration and sanctuary cities, Lee, Scott and Hennessy said San Francisco’s public safety agencies will not enforce federal immigration law and that the city “declines to participate in any agreements” noted in the two executive orders Trump signed at the White House last week.

Both of Trump’s orders “empower State and local law enforcement agencies across the country to perform the functions of an immigration officer in the interior of the United States to the maximum extent permitted by law.”

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But Lee, Scott and Hennessy say in the letter to Homeland Security Secretary John Kelly that it is “in the interest of public safety” that San Francisco officers and deputies do not enforce federal immigration law.

“Our community policing efforts are effective only if we have trust and cooperation of the communities we are charged to protect,” they wrote. “Pressing local jurisdictions to become entangled in federal immigration enforcement betrays that trust and undermines the work our public safety departments have done to improve relations with our residents. We will not jeopardize the public safety of our communities to do the job of the federal government.”

The letter continues: “Our law-abiding residents are safer when they can report crimes, get immunizations, and enroll their children in public school. If cities acquiesce to your demands to carry out immigration enforcement, we lose the trust of our communities.”

The Department of Homeland Security could not immediately be reached for comment Monday. But Lee, Scott and Hennessy said that the U.S. Supreme Court and other federal courts “have repeatedly emphasized that the administration of immigration laws is the responsibility of the federal government, not cities and states.”

“San Francisco will continue to honor valid criminal warrants and court orders as we always have,” they wrote.

San Francisco has had a sanctuary city policy in place since 1989 that limits local law enforcement’s cooperation with federal immigration agents in all but the most extreme circumstances. In 2013, the Due Process for All ordinance was passed, barring the city from holding jail inmates flagged by immigration agents past their release date.

Vivian Ho is a San Francisco Chronicle staff writer. Email: vho@sfchronicle.com Twitter: @VivianHo