The Ecuadorian president is being urged to reverse a ban on WikiLeaks founder Julian Assange using the internet or receiving visitors.
Among those signing a letter to Lenin Moreno are actress Pamela Anderson, musician Brian Eno, fashion designer Vivienne Westwood and former Greek minister Yanis Varoufakis.
The appeal has been co-ordinated by campaign group the Courage Foundation.
The Ecuadorian Government decided earlier this week to stop Mr Assange using the internet or social media from its embassy in London.
He has been living there for almost six years, believing he will be extradited to the United States for questioning over the activities of WikiLeaks if he leaves.
The internet ban followed a tweet from Mr Assange about the recent detention of Catalan president Carles Puidgemont in Germany.
The letter reads: "This is not just a matter of showing support and solidarity. We are appealing to all who care about basic human rights to call on the government of Ecuador to continue defending the rights of a courageous free speech activist, journalist and whistleblower.
"If there is no freedom of speech for Julian Assange, there is no freedom of speech for any of us -- regardless of the disparate opinions we hold."
A petition calling for the communications ban to be lifted has been signed by over 20,000 people.