Allegations that Russia hacked American institutions are false, Peskov said in an interview, and it's "high time for someone in the States to think, 'Are we that weak that a country can interfere in our domestic affairs and influence our electoral system?'
"This is unimaginable and someone has to say -- all this is not true. We have to be sober, let's come to our minds," Peskov said.
Questions about President Donald Trump's ties to Russia have consumed Washington since Trump assumed office. Much of the scrutiny is directed at meetings between Russian officials and people close to Trump before he took office
Peskov insisted Russia is not meddling in American politics.
"We don't have the slightest intention to interfere," he said. "The only thing I can tell you is that all this hysteria and public opinion, hysteria in official Washington and hysteria in American media, this is doing lots of harm to the future of our bilateral relations."
The United States is "global player number one," Peskov said, and Russia seeks a relationship with a stable government.
"For us, we are interested in having a predictable partner, a predictable vis a vis for the dialogue," he said. "And now when we unfortunately don't have a comfortable environment for our dialogue, of course it is a great pity."
Peskov said he's disappointed Russia has become such a political issue in the United States.
"We're really sorry about the situation that we are facing now. It is emotional extremism, of trying to make a toxic country out of Russia, to make a toxic ... ambassador out of Russia's ambassador," he said.
Sergey Kislyak, Russian ambassador to the United States
, has been scrutinized for his dealings with Trump's short-lived National Security Adviser Mike Flynn and two meetings with Attorney General Jeff Sessions.
Diplomacy can recover, Peskov said.
"I think yes," he said. "Let's not think in categories of one day, one month or even one year. Let's be a little bit more broad-minded. Let's be at least like our Chinese friends. They think about tens of years, hundreds of years, so inevitably we'll have our relationship normalized."
In early January, then-President Barack Obama took unprecedented steps to retaliate against alleged Russian interference in the 2016 election.
The administration described Russia's involvement as "Significant Malicious Cyber-Enabled Activities" and sanctioned four Russian individuals and five Russian entities for what it said was election interference. The administration also ordered 35 Russian diplomats to leave the country and two Russian compounds were to close.