The wide-ranging interview conducted in New York on Wednesday was the first time that Prime Minister Rajoy has answered questions about the most recent corruption scandal to rock his party.
He was asked about the investigation launched this week into the destruction of laptops belonging to jailed former party treasurer Luís Bárcenas.
The computers, said by Bárcenas to contain evidence that Rajoy and other senior Popular Party (PP) officals had received illegal payments, were found to be missing their hard drives when received from party headquarters.
Spain's National Court is now looking into a possible cover up.
Rajoy denied any knowledge of the matter and said: “I don’t know if they were there, if they had been there, or if someone removed them. I absolutely do not know.”
He responded to questions about the alleged illegal party fundraising that Bárcenas claims financed Rajoy's 2011 election campaign by saying, "There hasn't been any illegal financing."
"There are things that can’t be proven," he added.
Rajoy denied receiving illegal payments in parliament on August 1st but has since refused to answer questions on the subject from either lawmakers or journalists.
Antonio Hernando, Secretary of Institutional Relations and Regional Policy of Spain's Socialist Party, accused the government on Thursday of trying to 'gag' Bloomberg TV, according to online daily El Plural.
He alluded to comments made by journalist Javier Ruíz that "pressure" had been applied by the government to remove the sections of the interview relating to the Bárcenas scandal.
Bloomberg was said to have resisted and it was alleged that the channel "defended its journalism".
Hernando referred to Rajoy's recent reluctance to hold press conferences in person and his widely-lampooned statements delivered to journalists via plasma TV screens to question the impact on Spain's image of Rajoy's visit to the United States.
"You can understand why the president, in Spain, doesn't give press conferences or interviews, because when he comes out from behind the plasma he gets caught out, and he's been caught out on a television show watched by very important people in the world."
He added: "The business community has seen a president who has gone to sell the benefits of the Spanish economy but who has ended up admitting not that his party's financing was not illegal but that it couldn't be proven to be so in parliament."