Biden administration officials, worried that a new freeze on evictions might be struck down in federal court — and racing to prevent a national crisis — are increasingly turning to state courts to help deliver billions in federal housing aid.

On Wednesday, Attorney General Merrick B. Garland held a virtual meeting with 35 state Supreme Court justices in an effort to encourage them to use every tool at their disposal to avert or delay evictions by ensuring landlords and tenants have access to a $47 billion fund allocated by Congress.

Only about $3 billion of that cash — roughly 7 percent — had been allocated by June 30, according to the Treasury Department, which oversees the program.

“State courts are on the front lines of this crisis,” said Associate Attorney General Vanita Gupta, who has been overseeing the department’s efforts on evictions.

The effort to pay off back rent accrued during the pandemic has been hampered by resistance among some owners, who would rather evict nonpaying tenants than wait for federal payments, and sluggish efforts by states to create an infrastructure to distribute the largest allocation of housing funding in generations.

White House officials cited the need to buy more time for the aid program, along with public health concerns stemming from the Delta variant of the coronavirus, in drafting the new moratorium after the old one expired on July 31.

During Wednesday’s meeting, Mr. Garland cited several state initiatives as models for localities to follow, including an order by Michigan’s State Supreme Court requiring courts to stay eviction proceedings for up to 45 days to allow tenants to complete applications for rental assistance, according to Justice Department officials.

Another effort Mr. Garland singled for praise was a directive by the Republican-controlled Supreme Court in Texas, which modified notices sent to tenants who are sued for eviction to make sure they are aware of the benefits.

The state’s judicial training center also created instructions for local justices of the peace to divert landlords to the federal aid program whenever possible. That move, coupled with a joint federal-state effort to simplify application forms, is already showing some results, said Chief Justice Nathan Hecht.

“I’ve been on the bench for 40 years, and to tell the truth, judges historically did not see these kinds of programs as having anything to do with them, but that is changing,” Chief Justice Hecht said in an interview.

“The key to the whole thing is that the application process has got to be easy, it’s got to be simple,” he added. “Landlords are frustrated, and tenants are facing the streets, and overall it’s a very tense time. So, we can’t be telling people it’s going to take six weeks to get your money.”

In addition to pressuring Mr. Garland to help speed the checks, the justices asked federal officials to prioritize the role of the judiciary in all aid programs — to allow state courts to more easily tap into relief money to hire landlord-tenant mediators and navigators to assist tenants who cannot afford counsel to understand their rights in court.