Mr Pieth said officials told him that they would have final say on whether to publish the panel's findings on the offshore tax evasion scandal.
Joseph Stiglitz, a Nobel Prize-winning economist, also resigned.
The seven-person panel was set up by Panama's government in April 2016 to improve transparency.
Speaking on the BBC's Newshour programme, Mr Pieth said he had received a letter from Panama's authorities stating that they would have the final say on whether to publish the panel's report.
"They told us they were going to decide in the end whether (the report) is going to be publicised or not," he said.
"I think that the official Panamanians were in a state of denial. They were basically saying 'well, what we've been seeing in the Panama Papers is something that you observe everywhere in the world.'"
Mr Stiglitz also told Reuters news agency he was concerned that the panel's final report would not be published.
"We can only infer that the government is facing pressure from those who are making profits from the current non-transparent financial system in Panama," he said.
In a statement, Panama's Ministry of Foreign Affairs referred to "internal differences" and said it had a "strong and real commitment to transparency and international cooperation".
The Panama Papers were investigated by hundreds of investigative journalists, including staff from the BBC.
The documents were leaked from Panamanian law firm Mossack Fonseca and revealed how clients from around the world were able to launder money, dodge sanctions and avoid tax.
Those implicated included politicians, current and former national leaders, sports stars and celebrities.
Mossack Fonseca said it had been hacked by servers based abroad and filed a complaint with the Panamanian attorney general's office.
The company said it did not act illegally and that information was being misrepresented.
Eleven million documents held by the Panama-based law firm Mossack Fonseca were passed to German newspaper Sueddeutsche Zeitung, which then shared them with the International Consortium of Investigative Journalists. BBC Panorama and UK newspaper The Guardian were among 107 media organisations in 76 countries which analysed the documents. The BBC does not know the identity of the source
The Swiss anti-corruption expert, Mark Pieth, has told the BBC he resigned from the Panama Papers commission because of government interference.