The Spanish website Free Wikileaks urged rallies at 6pm local time in eight Spanish cities, including Madrid and Barcelona, while similar demonstrations were planned in Amsterdam, Buenos Aires, Mexico City, São Paulo, Bogotá and Lima.
In a manifesto entitled "For freedom, Say No to State Terrorism," the website demanded "the release of Julian Assange in the United Kingdom" and "the restoration of the WikiLeaks domain."
"Given that no one has proved that Assange is guilty of the offences he is accused of and that Wikileaks is not implicated in any of those," the website also urged that credit card giants Visa and MasterCard rescind their decisions to cut off donations from the whistleblowing website's supporters.
Assange is due to appear in a London court for a second time on Tuesday after being arrested on a warrant issued by Sweden. Prosecutors there want to question him about two women's allegations of rape and sexual molestation.
WikiLeaks insists the allegations are politically motivated because the website has enraged Washington and governments around the world by releasing a treasure trove of 250,000 confidential US documents, believed to have been supplied by a junior US army intelligence analyst.
The 39-year-old Australian has been transferred from the main section of Wandsworth prison to an isolation unit, according to Jennifer Robinson, a member of his legal team.
In the Netherlands, 75 people gathered in central Amsterdam to show their support for WikiLeaks, police spokesman Rob van der Veen told AFP.
The Amsterdam rally was sponsored by the Pirate Party of the Netherlands "to call for protection of freedom of the press" and "to express displeasure with the attempt to silence" sites such as WikiLeaks.
Assange supporters in Lima scheduled their demonstration outside the British embassy.
Meanwhile, new leaked US diplomatic cables revealed a row between the Vatican and Ireland over a child abuse inquiry.
The Holy See hit back after cables released by WikiLeaks indicated it had refused to cooperate with an Irish probe into child sex abuse by Catholic priests in Dublin.
According to another leaked cable made available to The New York Times and other news organizations, US diplomats believe that some top members of the Vatican's hierarchy still harbor anti-Semitic views.
"Naturally, these reports reflect the perceptions and opinions of the people who wrote them and cannot be considered as expressions of the Holy See itself, nor as exact quotations of the words of its officials," the cable stated.
"Their reliability must, then, be evaluated carefully and with great prudence, bearing this circumstance in mind," it added.
In other disclosures, mining giant BHP Billiton was said to have lobbied the Australian government hard to bring down a proposed $19.5 billion deal between rival Rio Tinto and China's Chinalco.
Spokesmen for BHP and Rio Tinto refused to comment on the US diplomatic cable published in The Sydney Morning Herald on Saturday.
Meanwhile, Assange's attorneys complained that their client was getting no recreation time in the prison and was having difficulties getting phone calls out.
"He is on his own," said Robinson.
The former computer hacker was not allowed to have a laptop in his cell, but his lawyers have requested one.
Assange was described as in "very good" spirits but "frustrated" that he could not answer the allegations that WikiLeaks was behind cyber attacks launched on credit card firms that have refused to do business with the website.
"He told me he is absolutely not involved and this is a deliberate attempt to conflate WikiLeaks, which is a publishing organisation, with hacking organisations which are not," Robinson said.
Separately, Assange's mother said she was worried for her son because "massive forces" were ranged against him. She dismissed the rape accusations, but told Australia's Seven Network she was concerned about what would happen to him.