Republican presidential candidate Donald Trump has appealed to Russia to uncover and release thousands of emails of his Democrat rival Hillary Clinton.
Mrs Clinton kept a private system for her emails while she was Secretary of State.
The emails were the subject of an FBI probe that found no basis for criminal charges despite what director James Comey called evidence that Mrs Clinton was "extremely careless" in her handling of classified information.
Mrs Clinton, who is is due to accept the presidential nomination on the last day of the party's convention, responded with a campaign statement accusing Mr Trump of posing a possible national security threat by urging Russia to commit espionage and influence the vote.
"Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing," Mr Trump, the Republican presidential nominee, told reporters. Mrs Clinton has said the emails she did not turn over to investigating officials were private.
In the same news conference, Mr Trump dismissed suggestions that Russia had sought to influence the US election by engineering the theft of embarrassing Democratic Party emails released by WikiLeaks last week.
The Democratic Party chairwoman, Debbie Wasserman Schultz, resigned on Sunday after the leaked emails showed party leaders favoring Mrs Clinton over her rival, Senator Bernie Sanders, for the presidential nomination.
Cyber security experts and US officials have said there was evidence that Russia engineered the release of the sensitive party emails in order to influence the presidential election.
"It is so far-fetched, it's so ridiculous," Mr Trump said of that theory. He suggested that China or some other party could be involved.
Russia has brushed aside suggestions it was involved. "I don't want to use four-letter words," Russian Foreign Minister Sergei Lavrov told reporters on Tuesday.
Mr Trump, who has praised Russian President Vladimir Putin in the past, said on Wednesday he did not know the leader. He said his closest interaction with Russia was selling a Florida home to a Russian for more than he paid for it.
Mr Trump supporter Newt Gingrich, a former speaker of the US House of Representatives, said on Twitter that the Republican candidate was joking when he suggested Russia hack Mrs Clinton's emails.
But Mr Trump repeated the call on Twitter, saying if anyone had Mrs Clinton's emails, "perhaps they should share them with the FBI!"
Mrs Clinton's campaign was not amused. "This is a national security issue now," campaign manager Robby Mook told reporters in Philadelphia.
"The idea that you would have any American calling for a foreign power to commit espionage in the United States for the purposes of somehow changing an election, we're now in national security space," he said.
Mr Trump's running mate, Indiana Governor Mike Pence, said the FBI would get to the bottom of the matter.
"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," Pence said in a statement.
During the pugilistic news conference at his Doral golf resort, which lasted more than 45 minutes, Mr Trump also said Mr Putin would respect him if he were elected and called current President Barack Obama, a Democrat, the most "ignorant" president ever.