Extremist supporters of Islamic State have been handing out leaflets promoting the establishment of a "Kahlifah" and calling on Muslims to "obey the Kahleef", on the streets central London this week, becoming threatening and abusive when challenged, according to witnesses.

One of the leaflets given out by the supporters calls for Muslims to "spread the Khalifah [caliphate] across the world," forming a new Islamic State governed by an Imam executing Islamic Sharia law.

Asmaa Al-Kufaishi, a British-Iraqi doctor, tweeted images she said were of the group canvassing around the busy shopping area of Oxford Street on Saturday, with materials using symbolism associated with the fundamentalist militant group Islamic State, formerly known as ISIS, which has declared a "caliphate" across parts of Syria and Iraq.

"My sister noticed the circle logo ISIS use on its flags and we then asked them why they were using it," Al-Kufaishi told Newsweek. "Initially they were cagey but then a guy with the ginger beard said there was nothing wrong with ISIS or anything they were doing in Iraq and Syria. That's how it started because I took offence to that and when we questioned him and his colleagues we were abused regarding our Iraqi nationality and the fact we were a different Islamic sect to them. We were told that we were kuffar (non believers) and that we should be killed like those Christians and Muslims in Iraq."

"When asked basic Islamic knowledge they had no idea. They are just a bunch of ignorant people who have used Islam as a way of terrorising others. they honestly didn't have a clue about the basic Islamic teachings and history," she added.

The leaflet says it is the responsibility of Muslims from around the world to pledge "Bayah [religious oath of allegiance] to the Khaleef" and "obey the Khaleef according to the Shariah". The leaflet goes on to argue "all those who can migrate and resettle should migrate", as "Muslims with the help of Allah have announced the re-establishment of the Khalifah".

Ghaffar Hussain, managing director at the Quilliam Foundation told Newsweek that the men handing out the leaflets were well-known extremists from Luton, probably associated with the al-Muhajiroun extremist network.

Hussain, who had spoken to someone who had witnessed the group distributing the leaflets near Oxford Circus on Tuesday but didn't want to speak to journalists, named one of the men as Ibrahim Anderson, formerly known as Roger Anderson, a white British convert to Islam. He said that the group had responded with abuse when challenged by passers-by. Newsweek could not independently verify the identities of those present at the protest.

"This is a very disturbing development but one that should not come as a surprise since we are aware that around 500 British nationals have joined up with ISIS already, said Hussain. "We need to have a zero tolerance policy towards ISIS supporters and recruiters in the UK."

The Metropolitan Police said that they were looking investigating whether the leaflets contained any criminal material but said they were not aware of any threats made against members of the public.

Last month pro-Islamic State supporters were filmed protesting in the Netherlands on two separate occasions in the Hague. This marked the first time the group's black flags were flown in Europe. The Dutch government has since made public displays of the flag illegal.

Last Thursday a banner bearing similar insignia to ISIS was hoisted off the gates of London's Will Crooks estate on Poplar High Street, the Guardian reported.

Islamic State now controls large parts of north and eastern Syria and northern Iraq, and have recently clashed with the Lebanese army, briefly taking a border town in Lebanon. The US has recently launched air strikes against the group to attempt to free thousands of Yazidis that Islamic State had surrounded on a mountain in Iraq, telling them they must convert to Islam or face death.