The often-delayed trial opened on Monday, with lawyers Juergen Mossack, Ramón Fonseca and other former employees of the firm facing money-laundering charges.
Mossack was present in the courtroom; lawyers for Fonseca said he was in a hospital in Panama.
Fonseca has said the firm, which closed in 2018, had no control over how its clients might use offshore vehicles created for them. Both Mossack and Fonseca have Panamanian citizenship, and Panama does not extradite its own citizens.
The two were acquitted on other charges in 2022.
The records were first leaked to the German daily newspaper Suddeutsche Zeitung, and were shared with the International Consortium of Investigative Journalists, which began publishing collaborative reports with news organisations in 2016.
US federal prosecutors have alleged that Mossack Fonseca conspired to circumvent American laws to maintain the wealth of its clients and conceal tax dollars owed to the IRS (Internal Revenue Service). They alleged the scheme dates to 2000 and involved sham foundations and shell companies in Panama, Hong Kong and the British Virgin Islands.