AP Photo/John Locher
The poll, released Tuesday by CNN, found that 48% of self-described Republican voters or leaners wanted someone other than Trump as the party's nominee.
The presumptive Republican nominee was backed by 51% who said they still want him to be awarded the nomination at the July convention in Cleveland.
CNN polled 409 registered voters. The sampling error was plus-or-minus 5%.
The Tuesday poll comes as Trump's overall poll numbers in a head-to-head matchup with presumptive Democratic nominee Hillary Clinton have plunged of late. Those numbers coincide with Trump's attacks against a federal judge based on his Mexican heritage, his controversial response to the Orlando terror attack, and the Monday firing of former campaign manager Corey Lewandowski.
And on Monday night, the release of Trump's May Federal Election Commission report showed the presumptive GOP nominee raised just about $3 million in his first month since sealing up the Republican bid. Trump had roughly $1.3 million in cash on hand at the end of the month.
By comparison, presumptive Democratic nominee Hillary Clinton, who had yet to clinch her party's nomination, raised $28 million in May through the campaign and its "victory fund," finishing the month with $42.5 million on hand.
Some Republicans have openly discussed unbinding the delegates at the party's convention so that they may vote for whomever they choose, although that appears to be highly unlikely. Still, roughly 1,000 anti-Trump Republicans, including many delegates, held a conference call to discuss such matters Sunday night.