More than 1,000 protesters have taken to the streets in Sweden to demand an end to a spate of mosque fires, amid growing tensions over the rise of an anti-immigration party.

The demonstrations in Stockholm, Malmö and Gothenburg, the country’s three largest cities, came a day after what was believed to be the third arson attack on a mosque in a week.

“We want to send the message that these attacks … are a problem for all of society and not just Muslims,” Mohammed Kharraki, spokesman for Sweden’s Islamic Association said during the largest demonstration, in the Swedish capital of Stockholm.

“This is about people being denied their basic rights … Everyone needs to ask themselves, politicians and citizens if this is the kind of society they want.”

Witnesses reported seeing a man throw a petrol bomb at a mosque in Uppsala in the east of the country early on New Year’s Day, three days after a late-night blaze at a mosque in Esloev in the south. “Go home Muslim shit” was scrawled across the doors of the building.

On Christmas Day, five people were injured in a suspected arson attack on a mosque in Eskilstuna, west of Stockholm.

Police said they were bolstering security around mosques. “We are working flat out with the investigation but we have no leads to report yet,” a police spokeswoman, Lisa Sannervik, said.

According to the anti-racism magazine Expo, there have been at least a dozen confirmed attacks on mosques in Sweden in the past year and a far larger number is likely to have gone unreported.

In a government survey of hate crimes in November, two-thirds of Swedish Muslim associations said their buildings had been vandalised.

The minister for culture and democracy, Alice Bah Kuhnke, said the attacks were “aimed at intimidating and diminishing people”. “That’s why one of the most important things we can do is to not let ourselves be intimidated,” she told demonstrators in Stockholm.

Debate over immigration has intensified in the Nordic country, which is expected to receive a record 100,000 applications for asylum this year.

Last month, the Sweden Democrats – which doubled its support to 13% in September elections – came close to bringing down the left-green government over its liberal refugee policies.

The far-right party, which wants to slash immigration by 90%, has increased its support in opinion polls to about 16%.