Cameron on Thursday finally conceded he and his wife, Samantha, owned shares in Ian Cameron's Blairmore Holdings, before selling them for around £30,000 in 2010.
Snowden, who this time last week ridiculed Cameron for sidestepping questions on his taxes, entered the debate on the PM's future after AFP journalist Marc Burleigh shared a tweet he had sent saying, "the next 24 hours could change Britain".
In response, Burleigh, wrote: "Probably overreach. Cameron: embarrassed, sure. Maybe even still not being full truthful. But implying resignation?"
Snowden, infamous for being a National Security Agency whistleblower, then replied saying the decision on Cameron's future was "up to the British public, not us".
He then went on to cite the outcome of the Panama Papers revelations in Iceland which resulted in Sigmundur David Gunnlaugsson stepping down as prime minister. The public had protested for several days calling for him to quit.
Snowden wrote: "In Iceland 10% of all voters were in the streets within 24 hours for less."
On Friday morning the hashtag #resigncameron was top trend on Twitter, something Snowden also alluded to in a tweet where he said the public needed to do more than just "hope" for that outcome.
He wrote: "UK Twitter right now: 'Let's hope Cameron resigns.' With respect, hope is not a strategy."
A protest is due to take place on Saturday outside Number 10 - demanding Cameron close the UK's tax havens.
In an interview with ITV News on Thursday, Cameron insisted it was a "fundamental misconception" that Blairmore was set up to avoid tax, saying his father was being "unfairly written about".
He also said that while his and Samantha's profit from the scheme was "subject to all the UK taxes in the normal ways" - it came to just below the threshold at which capital gains tax would have applied.
Number 10 said the Camerons bought their holding in April 1997 for £12,497 and sold it in January 2010 for £31,500.
The annual personal allowance for an individual in 2009-10 was £10,100 - meaning jointly the profit was just outside the threshold.
Cameron, who has been a prominent campaigner for increased tax transparency, also repeated his willingness to publish his own tax returns.
Downing Street later confirmed this will take place "as soon as possible".
Cameron has made four statements since the “Panama Papers” were leaked on Sunday, and said repeatedly he did not benefit from the Blairmore fund.
Many questioned whether the series of “non-denial denials” suggested he had reaped dividends previously.
In an interview with ITV News’s Political Editor Robert Peston, Cameron admitted he “should deal with the past”.
He said: “Of course I did own stocks and shares in the past - quite naturally because my father was a stockbroker.
“I sold them all in 2010, because if I was going to become Prime Minister I didn’t want anyone to say you have other agendas, vested interests.
“Samantha and I had a joint account. We owned 5,000 units in Blairmore Investment Trust, which we sold in January 2010. That was worth something like £30,000.”
The revelation came after the Tory party leader’s father was named in the massive leak of more than 11 million documents from Panamanian law firm Mossack Fonseca.
Ian Cameron, who passed away in 2010, was a director of Blairmore Holdings Inc, an investment fund run from the Bahamas, which oversaw tens of millions of pounds on behalf of wealthy families. In its 30-year history, Blairmore has never paid a penny of tax in the UK on its profits.
Downing Street initially said the issue was a “private matter”.