New South Wales police have been moved to reassure Australians that text messages claiming members of Islamic State (Isis) are knocking on people’s doors and marking Christian houses are a hoax, as concerns grow about the threat the extremist group poses.

The text message states: “There are members if Isis going door knocking on homes. They greet you with ‘Salam Alaykom’, and then pretend they are trying to collect money for orphans. They come with a black folder and ask you if you want to donate. I have just had one approach me at home just 2 hours ago. Please - do NOT Talk to them or open for them.”

The message, which references areas in the south-west suburbs of Sydney, exhorts people to “spread the word” and apparently convinced enough people for the police to feel compelled to tell them that there was no truth in it. In a tweet on Friday, the police included a picture of the offending text message with “FALSE” written in bold red letters across it. An accompanying message said: “Don’t be fooled by social media myths exploiting the current political climate.”

Pls RT - Don't be fooled by social media myths exploiting the current political climate. #mythbuster pic.twitter.com/Kc9PQn1Mha — NSW Police (@nswpolice) September 26, 2014

Tensions in Australia were raised this week by the shooting dead of terror suspect Abdul Numan Haider in Melbourne after he stabbed two police officers. The country’s prime minister, Tony Abbott, has plans for tough new anti-terrorism legislation and this month the government, which has committed a 600-strong military force to the US-led coalition against Isis, raised the country’s terrorism alert level to high for the first time in 11 years.

Islamic leaders have condemned threats Isis has made against Australia and urged Muslims to assist the police, but they have also expressed concern about a number of anti-Muslim incidents. In Brisbane, the words “get the fuck out of our country” were spraypainted on the side of a prayer centre.

Sheikh Abdul Azim, the president of the Australian National Imams Council, said: “There is some tension in the community. We want people to calm down, take it easy and when you see a Muslim man or woman, don’t think they are your enemy. They are innocent people.”