While Republican presidential candidate Donald Trump is doubling down on his call for Russia to hack into his opponent's emails, a chorus of condemnation for such action came swiftly, including a rejection from his own vice presidential running mate.

During a Wednesday press conference in Florida Trump invited Russian hackers to infiltrate Democratic presidential candidate Hillary Clinton's email server.

"Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing," Trump said. "I think you'll be rewarded mightily by our press!"

He was referring to emails that went missing from the private server Clinton used while Secretary of State. Despite the lapse, the FBI concluded after a year-long investigation that prosecutors had no grounds to file charges against Clinton, or any of her aides.

Trump's appeal to Russia provoked an uproar not only from the Clinton campaign but from Republican leaders and Trump's own vice-presidential candidate.

Clinton's top advisor, Jake Sullivan, slammed Trump for encouraging Russia to trawl the former secretary of state's emails, describing his comments as a "national security issue."

"This has to be the first time that a major presidential candidate has actively encouraged a foreign power to conduct espionage against his political opponent," Sullivan said. "That's not hyperbole, those are just the facts. This has gone from being a matter of curiosity, and a matter of politics, to being a national security issue."

GOP rejects Trump call

Republican House Speaker Paul Ryan's spokesman Brendan Buck rejected Trump's call, saying Putin and the Russian government had no business meddling in the US election.

"Russia is a global menace led by a devious thug," Buck said in a statement. "Putin should stay out of this election."

And no sooner had Trump reaffirmed his appeal than his vice-presidential running mate, Mike Pence, rejected it.

"The FBI will get to the bottom of who is behind the hacking," Pence said in a statement. "If it is Russia and they are interfering in our elections, I can assure you both parties and the United States government will ensure there are serious consequences."

Before Trump's latest bombshell, President Barack Obama weighed in on the Republican candidate's relationship with Putin,

"Donald Trump has repeatedly expressed admiration for Vladimir Putin," Obama said during a sit-down interview with NBC News that aired Tuesday. "And I think that Trump's gotten pretty favorable coverage back in Russia."

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Security experts say it appears likely that Russian agents hacked into the email server of the Democratic National Committee over the past year. The claim is being investigated by the FBI, but Trump maintains he not bothered by such a prospect.

"No, it gives me no pause," the celebrity businessman said. "If Russia or China or any of those country gets those emails, I've got to be honest with you, I'd love to see them."

bik/kms, kl (AP, AFP, Reuters, dpa)