SAN FRANCISCO — President Trump’s executive order withholding funding from communities that limit cooperation with immigration authorities applies to a small pot of grant money, not the hundreds of millions of dollars that local governments say is at stake, a lawyer with the Department of Justice said Friday.

Acting Assistant Attorney General Chad Readler made the comments during a court hearing on lawsuits filed by the city of San Francisco and the county of Santa Clara against Trump’s order targeting so-called sanctuary cities.

Readler said the city and county were interpreting the order too broadly.

The funding cutoff applies to DOJ and Department of Homeland Security grants contingent on compliance with a federal law that prohibits local governments from refusing to provide people’s immigration status to federal authorities, he said.

The order would affect less than $1 million in funding for Santa Clara County and possibly no money for San Francisco, Readler said. The plaintiffs have argued that more than $1 billion was at stake for each of them.

Sarah Eisenberg, a deputy city attorney in San Francisco, disputed Readler’s claim, saying the city has money at stake.

Readler’s comments about the money appeared to catch US District Judge William Orrick by surprise. Orrick then questioned the point of the president’s executive order.

The administration was using a ‘‘bully pulpit’’ to highlight an issue it cares deeply about, Readler responded.

John Keker, an attorney for Santa Clara County, rejected Readler’s interpretation and said the order referred to all federal funds now received by local governments that don’t detain immigrants for possible deportation when they are due for release from jail.

Orrick did not immediately issue a ruling after Friday’s hearing.

Associated Press