Court documents revealed that the La Liga side paid €7.3m (£6.4m) between 2001 and 2018 to two companies which were owned by Jose Maria Enriquez Negreira.
UEFA are currently conducting an investigation, with the governing body having the power to ban Barcelona from the Champions League for the 2023-24 campaign.
Meanwhile, former Barcelona presidents Josep Maria Bartomeu and Sandro Rosell have also been hit with corruption charges as part of the investigation, but the club continue to insist that they simply paid for technical reports on referees, which is not a crime.
Speaking during a press conference on Monday, Laporta said that he is "fully convinced" that the club have never done anything "with the intention" of gaining an unfair advantage.
"Throughout its 123-year history, FC Barcelona has always been a model of fair play, both on and off the field. If we have won for so many decades, it has undoubtedly been as a result of talent, effort and knowledge," said Laporta.
"No campaign to discredit us will prevent us from continuing to be an organisation of reference in the world of sports, that is beloved and admired by millions of Catalans and many more millions around the world.
"I am fully convinced that FC Barcelona has never performed any act with the intention of altering the competition to gain an advantage.
"Consulting on technical-refereeing issues does not constitute any kind of illegal act. Consulting - as is done by the big clubs - was carried out transparently, with the corresponding invoices, at least in my first mandate as president.
"If there were any person or private entity outside FC Barcelona that had taken advantage of this context to commit irregularities, the club would be the first to fully investigate. Our image is at stake."
Prosecutors in Spain have accused Barcelona of fraudulent management, breach of trust and falsification of business documents, with the investigation into the payments beginning in May 2022.
"As far as I am told, the situation is extremely serious," UEFA president Aleksander Ceferin recently said. "So serious that it is, in my opinion, one of the most serious in football since I have been involved in it."
Barcelona are yet to mathematically secure qualification for next season's Champions League, but they are 25 points clear of fifth-placed Real Betis in the table with nine games left, while their advantage over second-placed Real Madrid is 11 points.