"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 foreign policy advisor, 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."
The response on social media was swift, with some commenters accusing Trump of treason.
At least one Republican appeared to brush Trump's comments off as a joke.
"The media seems more upset by Trump's joke about Russian hacking than by the fact that Hillary's personal server was vulnerable to Russia," Newt Gingrich wrote.
Trump's running mate, Indiana Gov. Mike Pence, said in a statement Wednesday that the focus should not be on whether Russia hacked the DNC but should instead be on "the basic fact that they've (Democrats) been exposed as a party who not only rigs the government, but rigs elections while literally accepting cash for federal appointments."
"The FBI will get to the bottom of who is behind the hacking," he said. "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."
A spokesman for House Speaker Paul Ryan says Russian President Vladimir Putin should stay out of the U.S. presidential election.
In a statement from Rep. Paul Ryan spokesman Brendan Buck, the speaker of the house called Rissa "a global menace led by a devious thug."
"Putin should stay out of this election," Buck said.