The documents, which were obtained by German newspaper Suddeutsche Zeitung, allegedly show how Mossack Fonseca has helped its clients launder money, dodge sanctions, and evade tax.
Links to some of the world's most powerful figures are contained within the leaked data - including 72 current or former heads of state.
"I think the leak will prove to be probably the biggest blow the offshore world has ever taken because of the extent of the documents," said Gerard Ryle, director of the International Consortium of Investigative Journalists, which has been analysing the data.
Around 11m documents were leaked in total, and the revelations will be broadcast on BBC Panorama on Monday night.
The law firm said it has operated "beyond reproach" for 40 years, and added: "Our firm has never been accused or charged in connection with criminal wrongdoing.
"If we detect suspicious activity or misconduct, we are quick to report it to the authorities. Similarly, when authorities approach us with evidence of possible misconduct, we always cooperate fully with them."