While competition is intense in many populous regions, rural areas and small towns have far fewer carriers offering plans in the law’s online exchanges. Those places, many of them poor, are being asked to choose from some of the highest-priced plans in the 34 states where the federal government is running the health insurance marketplaces, a review by The New York Times has found.

Of the roughly 2,500 counties served by the federal exchanges, more than half, or 58 percent, have plans offered by just one or two insurance carriers, according to an analysis by The Times of county-level data provided by the Department of Health and Human Services. In about 530 counties, only a single insurer is participating.

The analysis suggests that the ambitions of the Affordable Care Act to increase competition have unfolded unevenly, at least in the early going, and have not addressed many of the factors that contribute to high prices. Insurance companies are reluctant to enter challenging new markets, experts say, because medical costs are high, dominant insurers are difficult to unseat, and powerful hospital systems resist efforts to lower rates.