President Trump is locked in a tight battle with several leading Democratic presidential contenders in a handful of states that are likely to decide the 2020 election, according to polling released on Monday that showed former Vice President Joseph R. Biden faring the best overall in trial heats against Mr. Trump.

Mr. Biden held 1- or 2-point leads over the president among likely voters in Michigan, Pennsylvania, Wisconsin, Florida, and Arizona, while Mr. Trump held a 2-point lead in North Carolina, according to the New York Times/Siena College surveys.

Sen. Bernard Sanders of Vermont led Mr. Trump by 3 points in Michigan, but trailed the president by 1-4 points in Pennsylvania, Florida, Arizona, and North Carolina. The two candidates were even in Wisconsin.

Sen. Elizabeth Warren of Massachusetts trailed Mr. Trump by 2-4 points in Michigan, Pennsylvania, Wisconsin, Florida, and North Carolina. The two candidates were deadlocked in Arizona.

Mr. Trump carried all six states en route to his win in 2016.

Among a broader pool of registered voters, Mr. Biden led Mr. Trump by 2-5 points in Pennsylvania, Wisconsin, Florida, and Arizona, but trailed by 2 points in North Carolina. The two candidates were even in Michigan.

Mr. Sanders led by 1-2 points in Michigan, Pennsylvania, and Wisconsin, and Mr. Trump led the Vermont independent by 1-3 points in Florida, Arizona, and North Carolina.

Mr. Trump led Ms. Warren by 3-6 points in North Carolina, Florida, and Michigan, and the two candidates were even in Pennsylvania and Wisconsin. Ms. Warren led by 2 points in Arizona.

The survey of 3,766 registered voters was conducted from Oct. 13-26 and has a margin of error of plus or minus 1.8 percentage points.

The margin of error for an individual state poll is plus or minus 4.4 percentage points, except for Michigan, which is plus or minus 5.1 points.

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