Hillary Clinton has once again blamed Russian intelligence services for hacking the Democratic National Committee (DNC) computer system and accused Donald Trump of supporting Russian president Vladimir Putin.

In her first national interview since clinching the Democratic nomination, Clinton spoke to Fox News Sunday. The interview was taped in Pennsylvania on Saturday morning before Trump criticized a dead soldier’s father, Khizr Khan, who spoke at the Democratic national convention.

Clinton answered tough questions on Benghazi, her emails and her campaign and policies, and focused her own attack on her opponent’s alleged links to Russia and Putin.

“We know that Russian intelligence services hacked into the DNC,” Clinton said, in her first interview with Fox in more than five years. “And we know that they arranged for a lot of those emails to be released and we know that Donald Trump has shown a very troubling willingness to back up Putin, to support Putin.”

Asked if she believed Putin wanted Trump to win the presidency, Clinton said she would not make that conclusion. “But I think laying out the facts raises serious issues about Russian interference in our elections, in our democracy,” she said.

The US would not tolerate that from any other country, especially one considered an adversary, Clinton said, adding: “For Trump to both encourage that and to praise Putin despite what appears to be a deliberate effort to try to affect the election I think raises national security issues.”

The hack of the DNC computers has also affected the Clinton campaign and the Democratic Congressional Campaign Committee. For about five days a hacker accessed an analytics data program maintained by the DNC that was used by the Clinton campaign to conduct voter analysis, said an aide familiar with the matter.

According to an outside cybersecurity expert for the Clinton campaign, the campaign is confident the hack could not result in access to internal emails, voicemails and other internal communications and documents.

The hack led to the resignation of DNC chair Debbie Wasserman Schultz on the eve of the party’s convention, and inspired protests in Philadelphia over leaked emails that showed top DNC staffers had discussed ways to undermine Clinton’s primary opponent, Bernie Sanders.

The FBI is investigating and federal sources have indicated that Russian intelligence sources may be to blame. On Wednesday, Trump appealed to Russia to find 30,000 “missing emails” from the private server used by Clinton when she was secretary of state. He later said he had been being “sarcastic”.

The billionaire’s campaign has rejected all claims of links to Russia and Putin. While surrogates such as campaign chair Paul Manafort and Alabama Senator Jeff Sessions appeared elsewhere on the Sunday shows, an interview with Trump, also recorded on Saturday, was broadcast on ABC’s This Week. He repeated: “I have no relationship with Putin. I have no relationship with Putin.”

Asked about a comment from 2013 in which he said: “I do have a relationship” with Putin, Trump said: “Just so you understand, he said very nice things about me. But I have no relationship with him.” He added: “I don’t think I’ve ever met him. I never met him. I don’t think I’ve ever met him.”

Trump was asked about his recent comments disparaging Nato allies, the softening of the Republican platform on Russia and Ukraine and his equivocations on Russia’s annexation of Crimea, the subject of US sanctions and United Nations disapproval.

“But you know,” he said, “the people of Crimea, from what I’ve heard, would rather be with Russia than where they were. And you have to look at that, also. Now, that was under – just so you understand, that was done under Obama’s administration.

“And as far as the Ukraine is concerned, it’s a mess. And that’s under Obama’s administration with his strong ties to Nato. So with all of these strong ties to Nato, Ukraine is a mess. Crimea has been taken. Don’t blame Donald Trump for that.”

He also said: “If our country got along with Russia, that would be a great thing. When Putin goes out and tells everybody, and you talk about relationship, but he says, ‘Donald Trump is gonna win. And Donald Trump is a genius.’ And then I have people saying, ‘You should disavow.’ I said, ‘I’m gonna disavow that?’

“But when Putin says good things, and when we have a possibility of having a good relationship with Russia … I think that’s good.”

Asked about the removal from the GOP platform a call for supply of lethal weapons to Ukraine for defense purposes, Trump said: “I wasn’t involved in that. Honestly, I was not involved.”

Host George Stephanopoulos said: “Your people were.”

Trump said: “Yeah. I was not involved in that. I’d like to … I’d have to take a look at it. But I was not involved in it … They softened it, I heard. But I was not involved.”

One of Trump’s people, Manafort, previously worked for Viktor Yanukovych, the former president of Ukraine and a Putin ally who now lives in exile in Russia. Appearing on NBC’s Meet the Press, he said he had no influence on the platform committee and the change “absolutely did not come from the Trump campaign”.

<!–[if IE 9]><![endif]–><!–[if IE 9]><![endif]–>Donald Trump

Donald Trump said: ‘If our country got along with Russia, that would be a great thing.’ Photograph: David Zalubowski/AP

On the same program, Clinton campaign manager Robby Mook said: “Espionage is never a laughing matter. And in fact, this is not a political issue … this is a matter of national security now. And I find it very frightening that Donald Trump is encouraging any foreign power to breach a campaign and try to influence the outcome of the election.”

Trump also told ABC he did not owe any money to Russian institutions or individuals, but repeated that he would not release his tax returns in an attempt to prove this. “Will I sell condos to Russians on occasion?” he said. “Probably. I mean, I do that. I have a lot of condos. I do that. But I have no relationship to Russia whatsoever.”

Told by Stephanopoulos that Richard Nixon had released his tax returns, Trump, who has made Nixonian tropes about law and order and slogans such as “the silent majority” a central part of his campaign, said: “Don’t use Richard Nixon as necessarily the guide, OK?

“I mean, you know, it’s an interesting person to use. But don’t use it.”