"They [Russian hackers] have infiltrated both parties at the national level," McCaul told CNN in an interview on Wednesday.
However, the Chief Strategist and Communications Director for the RNC Sean Spicer denied the hacking claim in a Twitter message.
So far, no documents have been leaked from the RNC and the Federal Bureau of Investigation (FBI) is looking into the intentions behind the attack, McCaul added. He also called on President Barack Obama to "come out very hard against Russia for having any role to undermine our election system and come out hard condemning these actions and taking a full retaliatory response to Russia."
The Kremlin has called other recent claims that Russia is involved in hacking the Democratic National Committee (DNC) or that it wants to influence the US presidential election — absurd.