Even as Anthem, one of the nation’s largest insurers, reported an improved financial picture for the last year, the company warned on Wednesday that it would consider leaving some federal health care marketplaces or raising its rates sharply if the government does not continue subsidies to help low-income people.

Joseph R. Swedish, the company’s chief executive, set a deadline of early June for a decision on the subsidies, saying Anthem would weigh increasing rates by at least 20 percent next year.

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