Broad support from women and minority voters has helped Hillary Clinton open an early lead over Donald J. Trump nationally, according to a new poll released on Monday.

A Monmouth University survey found that 47 percent of registered voters back Mrs. Clinton, the presumptive Democratic presidential nominee, while 40 percent support Mr. Trump, the Republican Party’s standard-bearer. The survey is the latest in a succession of recent polls that show Mrs. Clinton having an advantage, as Mr. Trump’s campaign has sputtered amid internal strife and an array of provocative public comments.

“Clinton has the advantage as the general election campaign kicks off, particularly in key swing states,” said Patrick Murray, director of the Monmouth University Polling Institute, in a statement. “However, all signs point to 2016 turning out the most polarized electorate in memory.”

The lack of diversity that comprises Mr. Trump’s core supporters has become a problem for his general election prospects. The poll found Mrs. Clinton drawing the support of 72 percent of minority voters and 57 percent of female voters. Mr. Trump holds more modest leads among men and white voters.