A majority of Republican and Republican-leaning voters trust presumptive GOP nominee Donald Trump more than House Speaker Paul Ryan to lead their party, according to a new NBC-SurveyMonkey poll out Tuesday morning.

According to the poll, 58 percent said they trust Trump more to lead the GOP, compared with 39 percent who chose Ryan. That figure is even higher among self-described "very conservative" Republicans, 63 percent of whom choose Trump over Ryan; only 34 percent of "very conservative" Republicans trust Ryan more to lead the party.

The poll comes as Ryan and Trump are engaging in a very public back-and-forth about the future of the party. Trump, the only remaining Republican candidate in the race, has suggested it's time for the party to recognize he's the GOP standard-bearer. Ryan, meanwhile, has met with Trump and called him "warm and genuine," but still has not endorsed Trump's candidacy and has said he has concerns about Trump's conservatism.

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In a general-election match-up, Trump trailed Democrat Hillary Clinton by just three points. Clinton took 48 percent in the poll, compared with 45 percent for Trump; last week, Clinton led by five points (49 percent to 44 percent).

Clinton's lead is fueled, as it has been during the Democratic primaries, by strong support among women and minorities. Among African American voters, Clinton leads Trump 84 percent to 9 percent; among Hispanics, the margin is 65 percent to 28 percent. Trump, meanwhile, leads among white voters by 14 points (53 percent to 39 percent). With women, Clinton leads by 11 points; among men, Trump leads by 11 points.

Interestingly, independents surveyed in the poll go for Trump by 8 points, 44 percent to 36 percent. Still, Clinton does better among self-described moderates: she wins them by 14 points, 53 percent to 39 percent.

The poll, conducted weekly, also finds Clinton's lead over Vermont Sen. Bernie Sanders growing slightly as the Democratic primaries continue. Among Democrats nationally, she leads Sanders by 14 points (54 percent to 40 percent), up from 12 points last week.

The poll, conducted online from May 9 to 15, surveyed 14,100 adults, including 12,507 registered voters. The margin of error is +/- 1.2 percentage points.