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The increasingly close race between Hillary Clinton and Senator Bernie Sanders is capturing the attention of the American electorate, according to NBC, which said that more than 10 million viewers tuned in to watch the Democratic presidential debate on Sunday night.

According to the network, 10.2 million people watched Mrs. Clinton, Mr. Sanders and Martin O’Malley debate in Charleston, S.C., two weeks before the Iowa caucuses. That was an increase from the two previous Democratic debates, which drew 8 million and 8.5 million viewers, respectively. The debate hosted by CNN in October remains the most watched of the cycle for Democrats, garnering more than 15 million viewers.

The Democratic candidates have two more debates left. Party leaders have been criticized for not holding more debates and for scheduling them on weekends, when fewer people are likely to watch.

Despite the increased viewership on Sunday night, the Democrats have failed to draw as much attention to their debates as the Republicans. Their crowded field, capped by the surprising success of Donald J. Trump, has brought record ratings (the first G.O.P. debate in August on Fox News, for example, drew 24 million viewers.)

NBC said that its digital platforms for the debate attracted an additional 1.2 million viewers.