The Supreme Court’s conservative majority appeared ready to scale back the long-standing deference given to the executive branch over regulatory policy in a pair of cases argued Wednesday with broad implications for federal agencies’ flexibility to interpret Congress’ words.

Changing what’s known as the Chevron doctrine could give courts more say in the decisions of federal agencies, an outcome that could ripple through environmental regulations, financial rules and health care benefit decisions. The high court’s decisions in the two cases could also impact presidents’ ability to shape executive policy and the standards courts use when evaluating what Congress meant in legislation.

In the two cases argued Wednesday — Loper Bright Enterprises v. Raimondo and Relentless, Inc. v. Department of Commerce — the challengers asked the court to overturn the Chevron doctrine that the federal appeals courts for the District of Columbia and 1st Circuit used to uphold a fishery inspection rule.

Solicitor General Elizabeth Prelogar, arguing the administration’s case to keep the doctrine, said overturning it would create a “convulsive shock to the legal system” because the courts, Congress and the public have relied on it for the last four decades.

Prelogar also argued that jettisoning Chevron would mean that the more than 800 U.S. district judges would be able to apply their own interpretation of every statute.

In more than three hours of oral argument in the two cases, Republican appointees to the court frequently pushed back on that idea. Justice Brett M. Kavanaugh argued that the doctrine has meant less stability in the legal system as each administration brings in its own interpretation of the law.

“The reality of how this works is that Chevron itself brings in shocks to the system every four or eight years,” Kavanaugh said. “That is at war with reliance. That is at war with stability.”

The Chevron doctrine is a nearly 40-year old legal test that encourages judges to defer to agency interpretations of ambiguous laws. The doctrine stems from a 1984 Supreme Court case, Chevron USA, Inc. v. Natural Resources Defense Council, Inc., that upheld a Reagan-administration decision by the Environmental Protection Agency led by Anne Gorsuch, the mother of Justice Neil M. Gorsuch.

Justice Ketanji Brown Jackson recused herself from the Loper Bright case because of her previous posting at the D.C. Circuit, and didn’t participate in that argument Wednesday.

But in the Relentless case, Jackson said jettisoning Chevron risked the court becoming a “super legislature,” deciding policy outcomes dressed up as legal disputes.

Justice Elena Kagan raised a similar concern.

“Congress knows that there are going to be gaps because Congress can hardly see a week in the future with respect to this subject, let alone a year or a decade in the future,” Kagan said, pointing out that Congress may prefer that agencies answer questions on difficult issues, citing artificial intelligence as an example.

Roman Martinez, arguing for the Relentless challengers, said the court’s interpretation of what a law means should be considered separately from what executive agencies decide to do with that interpretation.

Parts of the conservative legal movement and Republicans in Congress have targeted the doctrine for years, seeing it as emblematic of the power of the administrative state. Last year the House, with a Republican majority, passed a bill, 221-210 from Rep. Kat Cammack, R-Fla., that would overturn the doctrine, sending it to the closely divided Senate.

Paul D. Clement, arguing on behalf of the Loper Bright challengers, said the doctrine has also distorted Congress over the years, making it “virtually impossible” to legislate on difficult issues.

“It’s really convenient for some in Congress to avoid difficult questions and leave it to their friends in the executive branch,” Clement said. “Chevron is a big factor contributing to the gridlock.”

Clement said at any given time, half of Congress has a friendly executive branch, giving lawmakers little incentive to compromise with the other party on difficult issues and risk a primary challenge.

Justice Amy Coney Barrett pushed Prelogar to lay out how the court could handle the fallout of rolling back Chevron, asking whether a new test could be written in a way that preserves the dozens of Supreme Court decisions that relied on the old doctrine.

But Prelogar said litigants would “come out of the woodwork” to challenge decades-old decisions under a new standard. Prelogar also pointed out that Congress has written laws for decades with the assumption that they would be evaluated under the Chevron standard.

“Congress could modify and overrule Chevron but never has,” Prelogar said.

In recent years, the Supreme Court has issued several decisions reining in executive power, including unveiling the “major questions” doctrine. That doctrine, first used to strike down a greenhouse gas emission rule, holds that Congress must provide explicit authorization for agencies to act on issues of economic or political importance.

The court will likely decide the cases on the Chevron doctrine before the end of its term in June.