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Republican presidential candidate Donald Trump speaks during a campaign rally in Pittsburgh on April 13. | AP Photo Poll: One-third of GOP voters think Trump should run as independent if he loses nomination

Nearly two in three Republican voters (63 percent) want Donald Trump to support the Republican nominee if he does not get the party's nomination, even if he arrives in Cleveland with the most delegates but short of the magic number of 1,237, according to the results of a national CBS News poll out Thursday.

In the poll of 1,098 registered voters, one in three said they think Trump should continue his quest for the White House even if he is denied the Republican nomination, in the form of an independent or third-party run. That share jumps to 63 percent among Trump supporters.

Trump has been outspoken on his complaints surrounding the way delegates are allocated by individual state parties, particularly in Colorado, where Ted Cruz is likely to claim all of the state's 34 delegates. Trump is advocating that his supporters protest in Colorado on Friday.

Overall, Trump continued to lead in the national poll, though his lead over Cruz dropped by 7 points in the same poll over the past month. Trump took 42 percent to Cruz's 29 percent, while 18 percent said they support Ohio Gov. John Kasich.

The telephone poll, which was conducted April 8-12, has an overall margin of error of plus or minus 3 percentage points. The subsample of 354 likely Republican primary voters carries a margin of error of plus or minus 6 percentage points.