He said a report released by US intelligence agencies detailing the allegations was groundless.
It is the first official reaction from Russia since President-elect Donald Trump received the report on Friday.
The unclassified report contains allegations that Russian President Vladimir Putin had ordered the hacking of Democratic Party emails to damage Donald Trump`s Democrat rival, Hillary Clinton, and influence the election.
In his comments on Monday, Mr Peskov said Russia "categorically denied that Moscow had been involved in any hacking attacks".
"Groundless accusations which are not supported by anything are being rehearsed in an amateurish, unprofessional way. We don`t know what information they are actually relying on."
The claims amounted to a "witch-hunt", he added.
Mr Trump used the same "witch-hunt" term last week in a New York Times interview to disparage the hacking claims, which he has repeatedly rejected since winning the presidential election in November.
But his incoming chief of staff, Reince Priebus, told Fox News Sunday that the president-elect had accepted the findings of the report, which was presented to him by intelligence chiefs on Friday.
"He`s not denying that entities in Russia were behind this particular campaign," Mr Priebus added.
He did not clarify whether Mr Trump believed the report`s assertion that Russian President Vladimir Putin had directly ordered the hack.
Mr Trump described his meeting on Friday with National Intelligence Director James Clapper, CIA Director John Brennan and FBI Director James Comey as "constructive" and said he would ask, within 90 days of taking office, for a plan on how to stop cyber attacks.
But he declined to single out Russia, saying it was one of several countries, outside groups and people who "are consistently trying to break through the cyber infrastructure of our governmental institutions, businesses and organizations including the Democrat(ic) National Committee".
With less than two weeks until his inauguration, Mr Trump is under increasing pressure from both Democrats and Republicans to respond to the allegations.
President Obama has already expelled 35 Russian diplomats from US soil over the hacking. Russia said it would not reciprocate.
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