WASHINGTON (AFP) - Presumptive Republican presidential nominee Donald Trump cruised to victory in two more states on Tuesday (May 10), while Mr Bernie Sanders beat rival Democrat Hillary Clinton in West Virginia to bolster his argument for remaining in the race.

The substantial wins in West Virginia and Nebraska according to early results put Mr Trump ever closer to clinching the 1,237 delegates he needs to be declared the party's nominee at its convention in July.

"Thank you West Virginia!" and "Thank you Nebraska!" Mr Trump said in a pair of tweets.

Now the sole Republican candidate in the contest after his remaining rivals dropped out last week, Mr Trump is transitioning from the fierce primary battles with the likes of Mr Ted Cruz and Mr Marco Rubio to a general election showdown with Mrs Clinton, even amid deep Republican discord about the celebrity billionaire.

He has narrowed his picks for running mate, telling Fox News he is considering five vice-president options.

"I think they are excellent," he added. "I'll announce whoever it will be at the convention" in Cleveland, Ohio, Mr Trump said

With Republican concern about their nominee sizzling, a Quinnipiac University poll out on Tuesday showed Mr Trump closing in on Mrs Clinton's lead in two major battleground states - Florida and Pennsylvania - and overtaking her in swing state Ohio.

No candidate has won the presidential election without taking at least two of those three states.

Senate Majority Leader Mitch McConnell seized on the polls as a sign that Mr Trump will mount a strong challenge against Mrs Clinton.

"It's a long time till November, but the early indications are that our nominee is likely to be very competitive," Mr McConnell told reporters.

Despite Mrs Clinton's overwhelming delegate lead, Mr Sanders ensured the race would go on with his win in West Virginia, where he was ahead of Mrs Clinton by 11 percentage points with about a third of precincts reporting.

With eight contests remaining, "we think we have a good chance to win many of those states," Mr Sanders told supporters in San Francisco, according to CBS News. "We hope we can win some of them with big majorities."

Quinnipiac's poll also found that Mr Sanders, a democratic socialist who commands an enthusiastic following on the left, would do better against Mr Trump than Mrs Clinton in all three states if he were the Democratic nominee.

The 74-year-old Vermont senator, who defeated Mrs Clinton in Indiana, has mounted an unyielding come-from-behind challenge that has exposed weaknesses in the former secretary of state's campaign.

Although almost certain to win the Democratic nomination - she is only about 160 delegates short of that goal - Mrs Clinton's ability to excite young and white working-class Democrats going into the general election has been put in doubt by Mr Sanders's primary successes.

But she has used her campaign stops in Appalachia - including an event in Kentucky, which holds its Democratic primary on May 17 - as opportunities to win over blue-collar white voters.

"If I am so fortunate enough to be the nominee, I'm looking forward to debating Donald Trump come the fall," she said in Louisville.

"We can't be scapegoating and finger-pointing and blaming and demeaning and degrading and insulting our Americans."

In coal-mining West Virginia, Mrs Clinton shot herself in the foot in March by telling voters in neighbouring Ohio she would slash mining jobs and put coal companies "out of business."

She later apologised and suggested her remarks were misunderstood, but in a state where livelihoods have hinged on coal for generations, many are unconvinced.

While Mrs Clinton still has Mr Sanders to worry about, Mr Trump faces a rebellion within the Republican leadership over the insulting tone and shifting substance of his candidacy.

House Speaker Paul Ryan last week announced he was "not ready" to support Mr Trump, a rare rebuke that put the power struggles within the Republican Party on very public display.

Mr Ryan and other Republican congressional leaders were due to huddle with Mr Trump on Thursday in Washington, in highly anticipated meetings that could help gauge GOP support for the real estate tycoon.

Mr McConnell said he expected "a cordial meeting to discuss the way forward."

It may be thorny. A defeated Cruz ruled out a third-party bid, but when pressed by reporters as he returned to the US Senate, he declined to say whether he would endorse Mr Trump.

Mr Rubio said he would "support the Republican nominee" but would not offer an outright endorsement.

The Republican establishment is still reeling from Mr Trump's hostile takeover of the party, aghast at positions he's taken on trade, foreign policy and taxes that fly in the face of conservative dictums.

But Mr Trump has shown no sign of backing down, and some Republicans are looking to heal, embrace the nominee and turn to defeating Clinton in November.

"I think the party needs to come together," said Senator John McCain, the 2008 Republican nominee.