Donald Trump has opened up a 42 to 37 percent lead in a new Rasmussen Reports national poll that puts the two candidates against each other.

In early May, the same survey had the race virtually tied at 41 to 39 percent.

The survey comes a day after a Fox News poll released Wednesday also had Trump in the lead, although by a narrower margin, 45 to 42 per cent.

That poll nevertheless showed a rapid gain for Trump from April, when Clinton lead him by 48 to 41 per cent.

The Rasmussen poll shows both Trump and Clinton consolidating support among the party faithful – not withstanding an active #NeverTrump movement among disaffected Republicans trying to deny him a victory.

Trump has experienced poll gains since effectively wrapping up the GOP nomination

Donald Trump has opened up a 5-point lead over Hillary Clinton in the new poll

Anti-Trump forces have been trying to identify a possible third party conservative challenger to run against him, without success so far.

Trump gets 76 percent of the Republican vote, While Clinton gets 72 per cent of the Democratic vote.

The survey comes after a number of former rivals have fallen in line behind Trump, though House Speaker Paul Ryan of Wisconsin is still mulling his options after meeting with Trump last week.

Of particular concern for Clinton are independent voters, who go for Trump by 41 to 28 per cent in the survey.

Thirty one per cent of unaffiliated voters either back someone else or are undecided.

Clinton's ongoing primary fight against Senator Bernie Sanders keeps her from focusing on Trump

Trump is working to unify the Republican Party behind him after waging an angry campaign against elites from the outside.

He holds his first paid fundraiser Thursday in New Jersey, where he will help retire the campaign debt of former rival Gov. Chris Christie. Trump has also met with party luminaries like former Secretary of State Henry Kissinger, while announcing a slate of conservative Supreme Court picks.

Clinton, meanwhile, continues to wage a fractious primary campaign against Vermont Senator Bernie Sanders.

Clinton won the Kentucky primary on Tuesday but lost to Sanders in Oregon, while party regulars had an angry confrontation over delegates at a Nevada state party convention over the weekend.

Clinton's lead over Trump has also narrowed considerably in the pollster.com average, which incorporates many surveys. It now sits at 44 to 42 percent, a considerable narrowing from a month ago.