WASHINGTON — Attorney General William Barr has moved forward with a regulation changing the way immigration courts handle appeals, expanding the ability of those courts and the attorney general himself to issue decisions that bind the way all immigration judges must decide cases.

The final version of the regulation, which will be published Tuesday, backs away from several other changes that the department had proposed. Immigration advocates and attorneys raised concerns that those changes would give the appellate body too much discretion over precedent.

Barr’s first major regulatory change to the immigration courts continues efforts started by his predecessor, former Attorney General Jeff Sessions, to tighten the ways immigrants can pursue a right to stay in the country. As first reported by The Chronicle, the regulation was originally proposed during the George W. Bush administration and was revived under President Trump.

The version set for publication drops some of the more controversial provisions of the original proposal but expands the ability of the appellate body, the Board of Immigration Appeals, to issue binding decisions about immigration law.

A senior Justice Department official who briefed reporters on condition of anonymity Monday called the regulation a “cleanup rule more than anything else.” But, the official said, the administration believes the changes are important to make the courts “as efficient or as effective through the process as possible.”

The immigration courts are separate from the federal judiciary and exist entirely under the control of the Justice Department and attorney general. The lower courts hear immigrants’ arguments as to why they should be allowed to stay in the U.S. and decide whether they should be deported.

Appeals of those decisions are reviewed by the Board of Immigration Appeals. Under current law, those decisions remain unpublished, and thus not binding on the entire system, unless a majority of all 21 members of the board votes to publish them. According to the Justice Department, the board publishes an average of fewer than 30 decisions a year.

The new regulation creates another way for a decision to become binding: The attorney general can order it. Such a change could allow the attorney general to shape all immigration judges’ decisions by selecting which appellate rulings will become precedent.

Giving attorneys general such unilateral power, without requiring that they solicit input from parties with a stake in the outcome, could undercut a fair process, said Laura Lynch, senior policy counsel for the American Immigration Lawyers’ Association.

“Considering what is at stake with respect to these decisions, it is a grave mistake to allow the attorney general to expeditiously designate (immigration appeals court) decisions as precedent with the stroke of a pen,” Lynch said.

The association has advocated for the immigration courts to be removed from the control of the Justice Department and given independent status.

The final version of the regulation also expands the circumstances under which the Board of Immigration Appeals can hear cases for potential binding precedent, including “the need to resolve a complex, novel, unusual, or recurring issue of law or fact” in the immigration courts. That will allow the board to take up cases that the Justice Department views as a repeat issue in the lower courts. The regulation will also allow the board to weigh parts of a case that lawyers do not bring up at appeal.

One proposal that the administration chose not to pursue was expanding judges’ ability to issue cursory opinions with no written explanation. The final version also bowed to advocates’ and attorneys’ concerns and dropped a proposal that would have allowed two out of three appellate judges involved in a decision to make their ruling precedent, without having to win the approval of the full Board of Immigration Appeals.

The Trump administration has taken a keen interest in the immigration courts as it seeks to tackle the nearly million-case backlog of migrants seeking asylum and other rights to stay in the country. Such cases often take years to work through the system.

Sessions began using the attorney general’s power to refer cases to himself for review. Under immigration law, the attorney general has the final say over the immigration courts, similar to the Supreme Court in the federal judiciary.

Sessions issued several binding decisions that limited immigrants’ right to claim asylum for domestic violence and gang violence reasons, and he sped up the court process by reducing judges’ discretion to close or postpone cases.

The new rules will take effect 60 days from publication on Tuesday.

Tal Kopan is The San Francisco Chronicle’s Washington correspondent. Email: tal.kopan@sfchronicle.com Twitter: @talkopan