Majorities of voters in the key swing states of Colorado and Virginia back the legalization of marijuana for personal use and overwhelmingly support the legalization of medicinal marijuana, a new poll shows.

Fifty-four percent of Virginia voters support recreational pot compared to 41 percent who oppose it, and 62 percent favor it in Colorado, where marijuana is legal, compared to 34 percent opposed, according to results from a Quinnipiac poll released Tuesday.

In Iowa, voters are divided on the issue at 47 percent apiece.

But at least 86 percent of voters in each state support allowing adults to use marijuana for medical purposes.

“Voters in Colorado, Iowa and Virginia often disagree about the big issues of the day — taxes, government spending, gay marriage and abortion. Yet there is one thing that they pretty much agree upon across state lines — medicinal pot,” said Peter A. Brown, assistant director of the Quinnipiac poll.

“Huge majorities in all three states think marijuana should be legally available for medical use. In once-stately Virginia there is majority support for allowing adults to possess small amounts of the drug for personal use. Iowans are split on the question and more than 60 percent of Coloradans, who already enjoy legalized marijuana, are fine with it,” Mr. Brown said.

A Quinnipiac poll released last week showed similar numbers in the key presidential states of Florida, Pennsylvania and Ohio, where majorities of voters supported the legalization of marijuana and at least 84 percent of voters in each state supported the legalization of medical marijuana.

Twenty-three states and the District have legalized medical marijuana, and its recreational use is allowed in the District, Colorado, Alaska, Oregon, and Washington.

From March 29 to April 7, Quinnipiac University surveyed:

• 894 Colorado voters with a margin of error of plus or minus 3.3 percentage points

• 948 Iowa voters with a margin of error of plus or minus 3.2 percentage points

• 961 Virginia voters with a margin of error of plus or minus 3.2 percentage points.

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