The Kremlin strongman also suggested that attacks could be designed to appear to come from Russia in order to discredit the country.
"Apart from this claim which absolutely does not conform to reality, we have not seen any other information nor heard any arguments for the reliability of this information," Kremlin spokesman Dmitry Peskov told journalists.
"We resolutely deny the possibility that such a thing could have happened," he said, adding that he had not read the report.
The report by the National Security Agency was allegedly leaked by a private contractor just over a month after it was written and published Monday on The Intercept, an online news website which focuses on national security issues.
It depicted a hacking operation tied closely to Moscow's GRU intelligence directorate that targeted private US companies providing voter registration services and equipment to local governments.
President Vladimir Putin last week said that hackers can come from any country since they are "free people like artists" and conceded it was theoretically possible that a "patriotically minded" hacker could decide to act against those critical of Russia.
He insisted however that "we never get involved in this on a state level."
The Kremlin strongman also suggested that attacks could be designed to appear to come from Russia in order to discredit the country, while saying that in his opinion hacking cannot influence electoral campaigns in Europe, Asia or America.