Donald Trump at a campaign event at Trump National Doral Miami golf course in Florida on July 27. REUTERS/Carlo Allegri Donald Trump shocked political observers on Wednesday when he invited Russian hackers to find and publish Hillary Clinton's emails, and a senior spokesman for the Republican presidential nominee soon took to Twitter to do damage control.

"To be clear, Mr. Trump did not call on, or invite, Russia or anyone else to hack Hillary Clinton's e-mails today," Trump campaign senior communications adviser Jason Miller tweeted on Wednesday afternoon.

He continued: "Trump was clearly saying that if Russia or others have Clinton's 33,000 illegally deleted emails, they should share them w/ FBI" immediately.

Trump said at a press conference earlier in the day: "Russia, if you're listening, I hope you're able to find the 30,000 [Clinton] emails that are missing. I think you will probably be rewarded mightily by our press. Let's see if that happens. That'll be nice."

He was referring to the emails that Clinton says she deleted because they were personal in nature. She has been investigated for her use of a private email server while she served as secretary of state.

The remarks came after the Democratic presidential nominee's campaign said this week that Russian hackers were likely responsible for breaching the computer networks of the Democratic National Committee earlier this year and leaking emails of top officials to WikiLeaks for publication.

Miller accused Democrats of trying to change the conversation surrounding Clinton's use of a private email server while she served as secretary of state.

"Only reason we're talking about this is b/c HC deleted e-mails on home server & it's hurting her campaign," he tweeted. "D's trying to change subject."

Clinton's campaign issued a response to Trump's comments, calling the supposed hacking by Russia 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," senior policy adviser Jake Sullivan said in a statement. "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."

Some Republicans also pushed back on Trump's remarks.

A spokesman for House Speaker Paul Ryan issued this statement after the press conference: "Russia is a global menace led by a devious thug. Putin should stay out of this election."