Trump takes 19 percent support in the poll, with Walker at 17 percent. Former Florida Gov. Jeb Bush, with 12 percent, retired neurosurgeon Ben Carson, with 10 percent, and Sen. Marco Rubio, also with 10 percent, round out the top five.

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The margin between Trump and Walker is much slimmer than in a national Washington Post/ABC News poll released this week that found Trump leading Walker by 11 points, 24 percent to 13 percent.

The PPP survey, conducted Monday and Tuesday, indicates Trump may be facing some backlash for his criticism of Sen. John McCain's (R-Ariz.) military service.

Less than a quarter of Republicans in the poll, 22 percent, agreed with his comments over the weekend that McCain is not a war hero because he was held prisoner during the Vietnam War, while 50 percent disagreed with the reality TV personality.

Trump's favorability is also below 50 percent in the latest poll, though he leads among "very conservative" and moderate voters.

On the Democratic side, Hillary Clinton maintains a strong lead over her closest challenger, Sen. Bernie Sanders (I-Vt.), but the gap has tightened over the past month, according to the poll.

Clinton now leads Sanders 57 percent to 22 percent, an 8-point drop for Clinton and 13-point increase for Sanders since last month. Meanwhile, former Maryland Gov. Martin O'Malley has ticked down from 5 percent to 2 percent.

The survey of 1,087 U.S. primary voters was conducted July 20–21 via landlines and Internet surveys with a margin of error of 4.3 points for Republicans and 4.4 points for Democrats.