Donald Trump sensationally challenged Russia on Wednesday to hack into Hillary Clinton's emails as a furious Democratic campaign accused the Republican nominee of inviting foreign spies to meddle in the US presidential election.

At a sweeping news conference, the New York billionaire tried to undermine his White House rival, astonishingly implied that Vladimir Putin used a racial slur against President Barack Obama and promised a heyday of US-Russian relations under a Trump presidency.

His remarks provoked outrage from the Clinton campaign and left some Republicans wincing as his running mate hurriedly clarified that the party was not soft on Moscow and Trump tried to roll back his remarks.

Attacking Clinton as she prepares to accept her party's formal nomination, Trump turned his guns on a previous email scandal dating back to her time as secretary of state and more than 30,000 emails deleted on grounds of being personal and not related to her job.

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

The Clinton camp responded immediately and furiously.

"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 senior policy advisor Jake Sullivan said.

"This has gone from being a matter of curiosity, and a matter of politics, to being a national security issue."


Emails, emails, emails

While the FBI declined to recommend charges against Clinton over the email scandal, its conclusion that she was "extremely careless" with classified information has seen the Democrat lose her polling advantage to Trump.

The row spotlights deep US distrust of Russia, fueling yet another day of headlines about whether Russian agents may have hacked into Democratic Party emails which, once leaked, hugely embarrassed the Clinton campaign.

Those emails leaked by WikiLeaks showed the extent to which party leaders sought to undermine Clinton's rival Bernie Sanders, even questioning his religious faith, and forced the Democratic National Committee chair to resign.

The Clinton team blamed that leak on Moscow and accused Russia of conniving to get Trump elected. Obama also gave an interview refusing to rule out that Russia was trying to pull strings.


'Nothing to do with Russia'

Trump has frequently voiced admiration for Putin, who has been in power for 17 years as president or prime minister and refuses to grant unconditional support for NATO allies in the Baltic should they face hostile acts.

Moscow "probably isn't" behind the Democratic National Committee email hack, said Trump, who is yet to receive his first government intelligence briefing.

"I have nothing to do with Russia," he insisted.

Almost before Trump left the building, his running mate, Indiana Governor Mike Pence, sought to clarify that the Republican ticket was not in cahoots with Moscow, and attempted to shift the focus back to attacking the Democrats.

"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," he said.

"The American people now have absolute and further proof of the corruption that exists around Hillary Clinton. It should disqualify her from office."


Kremlin denies

Trump tweeted: "If Russia or any other country or person has Hillary Clinton's 33,000 illegally deleted emails, perhaps they should share them with the FBI!"

The Kremlin denies interfering in the US election.

"Russia has never interfered and does not interfere in internal affairs, especially in the electoral processes of other countries," Kremlin spokesman Dmitry Peskov told reporters on Wednesday.

Trump meanwhile said the Russian leader has no respect for Clinton or Obama.

"I think he does respect me," the real estate tycoon said, hinting that the Russian leader had used America's most charged racial slur against Obama.

"He mentioned the N word one time. I was shocked to hear him mention the N word," he said. "A total lack of respect for President Obama."

Trump spearheaded the so-called birther movement, which undermined America's first black president by claiming that he was not born in the United Sates.

"I would treat Vladimir Putin firmly," said the Republican nominee, adding that he would rather have a friendly Russia to "knock out ISIS together," referring to the Islamic State extremist group, which controls territory in Iraq and Syria.