Republican presidential nominee Donald Trump has been described as a national security risk after apparently encouraging the Russians to spy on government emails.
Mr Trump, 70, was speaking amid claims that Russia is meddling in the White House election.
It has also been alleged that Russian intelligence agencies are responsible for hacking the Democratic National Committee’s (DNC) computer servers.
Thousands of emails uploaded to Wikileaks seemed to confirm the DNC favoured Democratic Party nominee Hillary Clinton over her rival Bernie Sanders – something that resulted in the resignation of the committee’s boss Debbie Wasserman Schultz.
At a press conference at one of his Florida golf courses, Mr Trump said: “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.”
He refused to call on Russian president Vladimir Putin to stay out of the election, saying: “I’m not going to tell Putin what to do. Why should I tell Putin what to do?”
In response, Clinton advisor Jake Sullivan said: “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.”
“This has gone from being a matter of curiosity, and a matter of politics, to being a national security issue.”
Mr Trump also raised concerns about Mrs Clinton having access to security briefings because she has “probably (been) hacked”.
Republican and Democratic presidential nominees are allowed to attend some national security briefings so they are ready to govern if elected.
Mrs Clinton faced trouble earlier in the year after it was revealed she had used a private email server while secretary of state, but the FBI did not pursue the matter, with director Eric Holder saying they found no intent to expose classified information.