The Spanish-language website Free WikiLeaks said protests were scheduled to be held in Madrid, Barcelona, Valencia and Seville and at least three other Spanish cities.
Protesters held placards saying "Free Julian Assange" and "Truth Now," and chanted "freedom of speech."
The website also said demonstrations were planned Saturday in Amsterdam, the Netherlands, and in the capital cities of Colombia, Argentina, Mexico and Peru, as well as in Sao Paulo, Brazil.
"We seek the liberation of Julian Assange in United Kingdom territory," the organization said on the website. It urged protesters to gather at 6 p.m. (1700 GMT) in Spanish cities.
Assange remains in a British jail awaiting a hearing Dec. 14 at which he plans to fight Sweden's request to extradite him to face sex crimes allegations there.
One of his lawyers denied media reports that Assange was being held in isolation at Wandsworth Prison in London.
"He told me he had single cell," Mark Stephens said. "He has the ability to watch TV with other prisoners - which he doesn't do because he hates daytime telly. He takes his meals with other prisoners."
Stephens said lawyers met with Assange at the prison for an hour Thursday to prepare for next week's hearing.
The Free WikiLeaks website also calls for "the re-establishment of the WikiLeaks (wikileaks.org) Internet domain," and the restoration of Visa and MasterCard credit card services to enable the "freedom to move money" because no one has "proved Assange's guilt," or charged WikiLeaks with any crime.
Many U.S.-based Internet companies have cut their ties to WikiLeaks, including MasterCard Inc., Visa Inc., Amazon.com, PayPal Inc. and EveryDNS.
Those moves have hurt WikiLeaks' ability to accept donations and support publishing efforts.
On Friday thousands in Australia protested the treatment of Assange by their government and by the U.S.
CBS News' Ali Donaldson reports the government is standing by its view that the Wikileaks site is probably illegal. Supporters of Assange say the government has not done enough to protect an Australian citizen from persecution.
Organizer Antony Lowenstein called the Australian government's behavior "utterly outrageous."
The group has also raised money to buy full-page ads in The New York Times and Washington Times.
Sam McLean of Get Up said, "We're sending a message to President Obama and attorney general, that we want America to stand up for our shared beliefs, in presumption of innocence and freedom of information."
Police were told to expect 200 people at a rally in Sidney; within 24 hours 1,200 showed up.