Donald Trump denied any relationship with Russia on Wednesday, in response to claims that Moscow had hacked into the Democratic National Committee's email system and leaked emails that could benefit the Republican presidential candidate.

The emails cast a shadow over the Democratic convention that started Monday by raising questions about the impartiality of the party in the primary process.

DNC chairwoman Debbie Wasserman Schultz was forced to step down after the emails revealed a bias towards Hillary Clinton over rival Bernie Sanders.

US intelligence agencies reportedly believe Russia was behind the DNC hacking after the documents were published by WikiLeaks on Friday.

Trump, the Republican nominee, said the idea he was politically linked to Russia or the DNC hacking was "ridiculous."

"If it is Russia, which it's probably not, nobody knows who it is, but if it is Russia, it's really bad for a different reason, because it shows how little respect they have for our country," Trump said at a press conference.

Clinton has been involved in a separate controversy over her use of a private email server while secretary of state and Trump also sought to involve Russian intelligence agencies in that matter.

"Russia, if you're listening, I hope you find the 33,000 emails that are missing [from Clinton's server]. I think you'll be rewarded mightily by our press," he said.

Clinton's campaign responded later Wednesday, saying Trump's calls for another country to hack into US servers amounted to 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," Clinton's campaign said in a statement. "That's not hyperbole, those are just the facts."

James Rubin, a Clinton foreign policy advisor, said on the sidelines of the Democratic convention that Trump's remarks were "the clearest possible evidence of ... the fact that the nominee for the other party is unfit to be commander-in-chief."

However, Trump spokesman Jason Miller backed off on the statement within hours of the press conference.

"To be clear, Mr Trump did not call on, or invite, Russia or anyone else to hack Hillary Clinton's email today," spokesman Jason Miller wrote on Twitter. "Trump was clearly saying that if Russia or others have Clinton’s 33,000 illegally deleted emails, they should share them w/ FBI immed."

In December, before the Republican primaries began, Russian President Vladimir Putin said Trump was "absolutely the leader in the presidential race.”

Putin has since refrained from commenting, but said in June that he is looking forward to the improved Russian-American relations that Trump has promised.

Trump acknowledged Wednesday that Putin said a "nice thing" about him, but added that if Russia was involved in the email scandal, it was a more a show of disrespect for the current administration than any favoritism towards him.

"I don’t think Putin has any respect whatsoever for Clinton, but he does like me," Trump said. "I would treat Vladimir Putin firmly, but there's nothing I’d rather do than have Russia friendly so we can go knock out (Islamic State)."

Trump's running mate, Indiana Governor Mike Pence, said there will be serious consequences for Russia if it is behind the DNC hacking, but that the American people should focus more on the content of the emails.

"The Democrats singularly focusing on who might be behind it and not addressing the basic fact that they've been exposed as a party who not only rigs the government, but rigs elections while literally accepting cash for federal appointments is outrageous," Pence said in a statement.

"The American people now have absolute and further proof of the corruption that exists around Hillary Clinton."

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