A federal judge on Friday agreed to extend an order blocking the National Institutes of Health from reducing grant funding to institutions conducting medical and scientific research until she could come to a more lasting decision.

Judge Angel Kelley of the Federal District Court for the District of Massachusetts had temporarily blocked the Trump administration’s cuts from taking effect earlier this month, with that hold set to expire on Monday. That teed up an urgent hearing on Friday in which states and associations representing those institutions urged her to consider halting the cuts more permanently.

The stakes of the lawsuit were put in stark relief during one portion of Friday’s hearing that focused on “irreparable harm,” in which Judge Kelley asked both sides to explain whether the suspension of the funds amounted to an irreversible blow to the universities and hospitals across the country that depend on the funding.

The N.I.H. has proposed cutting around $4 billion in grants it provides for “indirect costs,” which it has described as tangential expenditures for things like facilities and administrators, and which it said could be better spent on directly funding research. The proposal envisioned reducing funding for those indirect costs to a 15 percent rate to all institutions that receive funds, which a lawyer for the government said was in line with that of private foundations.

But the coterie of lawyers representing the states and research institutions argued to the judge that the direct and indirect costs are often intertwined.

One lawyer asked Judge Kelley to consider a scenario of a researcher doing experiments directly funded through an N.I.H. grant, and a worker disposing of hazardous medical waste produced by all the experiments being run at that facility.

“It is equally important to the research that both of those people are paid to do their work,” the lawyer said. “The research couldn’t happen without that — nevertheless, one is classified as a direct cost, one is an indirect cost.”

Lawyers for the plaintiffs ticked through an array of adverse effects that could result from the pause in funding.

They asked the judge to consider the ramifications of potential layoffs of highly skilled staff members, such as veterinary technicians that oversee animal research and hospital nurses. They warned of clinical trials on new drugs being paused. They argued that many institutions would be unable to bring back employees they had lost once experiments and trials were forced to stop.

Brian Lea, a lawyer representing the government, said on Friday that the broad effects mentioned at the hearing were largely speculative, part of a “nonspecific aura of urgency” that research institutions had drummed up without showing concrete damages.

With universities in the middle of admissions season, the plaintiff lawyers described a chaotic environment in which both schools and Ph.D. applicants would need to reassess whether the projects they planned to pursue would be feasible. And they expressed fear for smaller universities that were not likely to be able to fill the unanticipated gap left in their budgets.

Even at larger schools with hefty endowments, the promise of government funding had already influenced big investments, the plaintiff lawyers said.

They pointed to a $200 million neuroscience lab at the California Institute of Technology, finished in 2020, that the university expected to pay for in part through the funding.

“There’s going to be a hole in the research budget at Caltech, and actually a big one,” a lawyer said.

The plaintiff lawyers said that other groups not involved in the lawsuit, such as associations of dental and nursing schools, had also become invested in the outcome, fearing disruptions to their own operations.

“Are you willing to agree that the plaintiffs will suffer harm?” Judge Kelley asked the government’s lawyer after hearing the long list of examples marshaled by the groups suing.

“Not irreparable,” Mr. Lea replied.

He said the states and associations suing the government had other means of recovering the lost funding, such as suing under the Tucker Act, which allows groups to sue the government in contract claims. He added that the 15 percent cap was in line with what private foundations such as the Gates Foundation often agree to.

Earlier, Mr. Lea repeated the government’s claim that capping “indirect funds,” for costs like buildings, utilities and support staff, at 15 percent was simply designed to free up more money to be allocated directly to researchers.

“I want to be clear about one thing at the outset: This is not cutting down on grant funding,” he said. “This is about changing the slices of the pie, which falls squarely in the executive’s discretion.”

Lawyers suing to stop the cuts said that capping indirect funds at 15 percent across the board was arbitrary, a standard for challenging agency decisions. They argued that institutions of different sizes naturally have different needs when negotiating with the government, and forcing all to adapt to a 15 percent maximum was unreasonable.

“A lot of this is driven by economies of scale, right?” one of the lawyers said. “The larger the institution you have, the bigger the building you have, the more you can house multiple projects within that one building — that’s going to change your ratio of direct costs or indirect costs,” she said.