WASHINGTON — Mayor Rahm Emanuel and Cook County Board President Toni Preckwinkle said they will stand firm on policies sheltering illegal immigrants even after Attorney General Jeff Sessions said Monday he will cut — or even “claw back” — Justice Department funds flowing to “sanctuary” cities, counties or states.

Sessions made his announcement at the start of the daily White House press briefing. It follows executive orders that President Donald Trump signed in January to build a border wall with Mexico and cut off federal funding to “jurisdictions that willfully refuse to comply” with immigration laws.

Emanuel has staunchly defended Chicago as a sanctuary city that welcomes immigrants. His spokesman, Matt McGrath, said in an email that nothing Sessions said will change City Hall policy.

“The administration’s plan to deny federal funds to cities that are standing up for their values is unconstitutional,” McGrath wrote.

McGrath did not say how much DOJ funding that Chicago might lose or whether the city would stop spending that money in anticipation that it might have to repay the federal government.

Preckwinkle spokesman Frank Shuftan said in an email, “As for General Sessions’ statement today, let’s be clear that we cooperate with other government entities to the extent required and permitted by applicable law. Persons arrested are routinely processed and information entered into the appropriate database. But in the absence of a criminal warrant we do not detain anyone after a judge determines that he or she should be released.”

“Most importantly, we are not agents of the federal government,” Shuftan added. “As such, and despite the threats made by General Sessions today, our position on ICE detainers remains unchanged.

“We believe it is appropriate for ICE to carry out its responsibilities through its own due diligence, but any effort by the president or members of his administration to compel localities to aid in federal immigration enforcement threaten the safety of our residents and, in our view, violate constitutional law.”

At stake is the risk of losing federal money if Sessions’ DOJ declares a local government not in compliance with federal law.  In the current federal budget year, the DOJ Office of Justice Programs is on track to distribute $4.1 billion in grants nationwide.

Seventy grants totaling $120.4 million are being sent to Illinois. Examples include a joint Chicago/Cook County Edward Byrne Memorial Justice Assistance Grant of $2,333,428; the Cook County Justice and Mental Health Collaboration, $243,012; and the Cook County South Suburban Safe and Thriving Communities Project, $1 million.

Besides Chicago and Cook County declaring sanctuary status, Evanston and Oak Park have sanctuary ordinances; Melrose Park has one in the works.

Evanston Police and the Northwestern University Police Department won $139,277 for a Body Worn Camera Implementation Program.

Emanuel’s office noted that Chicago has joined a coalition of of cities and counties that are asking a federal court to halt Trump’s executive order on sanctuary jurisdictions. On Sunday, that coalition filed an amicus — or friend-of-the-court — brief in San Francisco federal court in support of the County of Santa Clara’s lawsuit against the president.

“Chicago is proud to stand with 34 cities and counties across the country in asking a federal court to prevent the federal government from illegally withholding federal funds,” McGrath said.

Sessions on Monday cited criminal acts by several illegal immigrants in San Francisco and Denver as he discussed how sanctuary localities violate federal law.

“The president has rightly said this disregard for law must end,” Sessions said. “Today, I am urging states and local jurisdictions to comply with these federal laws. . . . Moreover, the Department of Justice will require a jurisdiction seeking or applying for Department of Justice grants to certify compliance with (federal law) as a condition of receiving these awards.”

Former President Barack Obama made a priority of enforcing immigration laws when it came to illegal immigrants with a criminal history or who posed a threat to public safety or national security, setting his policy in a June 17, 2011 directive known as the “Morton Memo,” authored by Immigration and Customs Enforcement (ICE) Director John Morton.

Federal prosecutors were told to exercise “prosecutorial discretion” and to handle illegal immigrants on a “case-by-case” basis during Obama’s tenure. Deportations jumped during Obama’s two-terms.

However, the Obama White House did not try to end the practice of localities, almost all run by Democrats, of declaring sanctuary status.

According to a report from the Department of Homeland Security, during the week of Jan. 28, 2017, through Feb. 3, 2017,  ICE ordered 3,083 detainers across the nation; only 13 or them were in Cook County.

Sessions said he is “urging” the localities to “rethink” sanctuary-city policies because “these polices make our cities and states less safe.”

“Department of Justice will also take all lawful steps to claw back any funds awarded to a jurisdiction that willfully violates 1373,” with the number a reference to federal law. “I strongly urge our nation’s states and cities and counties to consider carefully the harm they are doing to their citizens by refusing to enforce our immigration laws and to rethink these policies.”

The Illinois Coalition for Immigrant and Refugee Rights said in a statement that Sessions moves against illegal immigrants  will make catching criminals harder. “Communities like Chicago and Cook County have seen the wisdom of limiting police entanglement with immigration enforcement:  If immigrants are afraid to come forward to report crimes, the entire community is harmed,” the coalition said.

Omar Jadwat, director of the American Civil Liberties Union’s Immigrants’ Rights Project, said in a statement, “Despite the Trump administration’s bluster and threats, the federal government cannot coerce local police into becoming deportation agents, and should not try to scare local authorities into taking illegal actions that undermine public safety and subject them to liability.

Said Democratic National Committee chair Thomas Perez: The Trump “administration not only is trying to bully law enforcement and make them ICE agents, but they’re trying to bully immigrant families. This is not who we are as a country.”

Contributing: Mick Dumke