New York Gov. Andrew Cuomo on Monday issued emergency regulations aimed at deterring insurers from leaving the state’s Affordable Care Act exchange market as Congress weighs repealing former President Barack Obama’s signature health-insurance law.

The ACA, often dubbed “Obamacare,” set up marketplaces where consumers can buy coverage from different insurers and obtain federal subsidies to help with the cost. But the House of Representatives has passed legislation that would bring huge changes to the current exchange markets. The Senate is working on its own version of the bill.

Mr. Cuomo, a Democrat, ordered the state health department to bar health insurers that withdraw from the New York exchange market from participating in other state programs including Medicaid, an action that could pose a financial threat to some companies.

He also directed the state’s Department of Financial Services to require insurers in New York to continue covering medical services required under Mr. Obama’s law. It isn’t clear if a replacement for the ACA would ultimately mandate those coverage areas.

“These aggressive actions will make certain that no matter what happens in Congress, the people of New York will not have to worry about losing access to the quality medical care they need and deserve,” Mr. Cuomo said.

The state’s move comes as insurers around the country have warned about pulling back from the exchanges after taking financial losses and amid uncertainty in Washington about the future of the ACA.

Humana Inc. in February announced it would exit all the health-law marketplaces next year. Aetna Inc. has also said it is pulling out of the exchanges where it currently offers plans.

At least one state, Missouri, appears likely to have an area with no exchange insurers, after an announcement by Blue Cross and Blue Shield of Kansas City that it will stop offering marketplace plans in 2018.

Anthem Inc., a major insurer in New York, has said it is weighing the future of its exchange business nationwide and may pull back in at least some areas.

Alphonso David, Mr. Cuomo’s counsel, said in an interview Monday that insurers who leave the market will face “aggressive action” from the state.

Thomas Carroll, an analyst with Stifel Financial Corp. , said that given the size of New York’s Medicaid business, the state’s move could have a significant impact on insurers’ decision-making. Mr. Carroll said the action is likely to be imitated by other states looking to prop up their ACA marketplaces.

“The potential for Medicaid contracts now and in the future creates strong leverage,” he said.

Nevada has also moved to keep insurers in its exchange. Heather Korbulic, executive director of Nevada’s health-insurance marketplace, said Aetna has filed materials indicating it will offer plans there next year. She said Aetna agreed to enter the exchange as part of a contract to manage Medicaid plans in the state.

An Aetna spokesman declined to comment on its plans there.

Bill Hammond, a health-care analyst at the Empire Center, a conservative-leaning New York think tank, said that while Nevada offered “a carrot“ to an insurer to stay, Mr. Cuomo was offering “a stick” for leaving.

Mr. Hammond questioned Mr. Cuomo’s use of emergency regulations, which enables him to implement the regulations without a delay or public-commenting period. “I don’t think there’s an emergency here by any definition,” Mr. Hammond said. “Even if that law passed tomorrow, it doesn’t take effect until 2018,” he said, referring to an Obamacare replacement being considered by Congress.

Mr. Cuomo’s regulatory approach bypasses the state Legislature, but could be undone by another governor. The Democratic-led Assembly and GOP-led Senate didn’t comment Monday on the new regulations.

The Assembly earlier this year passed a statewide single-payer healthcare plan, but it has stalled in the more conservative Senate.

© 2017 Wall Street Journal