Anthem, one of the nation’s largest insurers and a major player in the individual insurance market created by the federal health care law, announced Tuesday that it would stop offering policies in the Ohio marketplace next year.

Although its departure would leave a small number of people — roughly 10,500 who live in about a fifth of the state’s counties — without an insurance carrier, the move was seized on by Republicans as more evidence that the markets are “collapsing” under the Affordable Care Act. President Trump, meeting with congressional leaders on Tuesday, said it was more proof that insurers are “fleeing and leaving” the marketplaces and added that it was essential for Congress to pass a bill repealing the health law this summer.

Republican senators said on Tuesday that they were trying to reach agreement on some major issues, especially Medicaid.

Senator John Barrasso, Republican of Wyoming, said that Republican senators spent much of a meeting on Tuesday with Vice President Mike Pence discussing health care. Mr. Barrasso outlined some differences with the bill that passed the House.