Five new self-professed Conservative members have been revealed to have posted Islamophobic or racist comment on Facebook, prompting fresh concerns about anti-Muslim sentiment in the Conservative party.

Messages seen by the Guardian refer to Muslims as “cavemen”, call for them to be “rounded up and returned to point of origin” and claim “most” of the religion’s followers are sex offenders.

One of the Tory supporters shared a racist image suggesting women only wear burqas because they are unattractive.

The five posters, all of whom claim to be Conservative members, are part of an unofficial Facebook group set up in support of Jacob Rees-Mogg, who chairs the party’s hard Brexit-supporting European Research Group. The Facebook page frequently features racist content. Each of the five have indicated in Facebook posts that they had joined the Conservatives, although the party refused to confirm whether they were members.

The development follows the Conservatives’ suspension last week of 14 other members over similar Facebook posts unearthed by the anonymous @matesjacob Twitter account, which also discovered the new material and passed it to the Guardian.

The Conservatives have come under sustained criticism over the issue, with the party chairman, Brandon Lewis, challenged over whether he had issued misleading statements in response to questioning about the number of complaints about Islamophobia.

Conservative peer Sayeeda Warsi, who has led calls for the Tories to hold an inquiry into the party’s handling of Islamophobia, said: “It is now well documented that my party’s response has been neither swift nor thorough. The experience of those that have complained is of a process that is opaque, unresponsive and a chairman’s office that lacks the political will to investigate and exclude those making racist and Islamophobia comments.”

According to a new definition of Islamophobia produced by the all-party parliamentary group on British Muslims adopted on Wednesday by the Labour party, it is “rooted in racism and is a type of racism that targets expressions of Muslimness or perceived Muslimness.”

On Sunday, the Labour mayor of London, Sadiq Khan, urged the Conservative party to adopt the same definition, saying he had frequently been subjected to Islamophobic abuse from Conservative members and supporters.

“I have lost track of the number of Conservative councillors and members that have been suspended or faced legal action as a result of making Islamophobic comments towards or about me,” he said.

Sadiq Khan has urged the Tories to adopt the same definition of Islamophobia as did the Labour party. Photograph: David Levene/The Guardian

The Guardian discovered a host of Islamophobic content posted on Facebook by members of 20,000-strong group set up in support Rees-Mogg, including those who have identified themselves as card-carrying Conservatives. The page is not officially affiliated to the politician.

In response to a thread warning about sharia law coming to Britain and a commenter writing “we going backwards now to please Muslims”, the claimed Tory member replied: “These people are cavemen. We are all told to be tolerant but I can’t be. I find them offensive on so many levels. They have no interest [in] integration and many cannot hide their dislike for us. Personally I’d like them rounded up and returned to point of origin.”

In a separate thread making light of Boris Johnson’s controversial remark that Muslim women wearing burqas “look like letterboxes”, he shared a racist picture in reply suggesting women who wear them are unattractive. The image depicts three Asian women with facial hair, adding the message: “Ban the Burka. You must be Fucking joking.”

A second self-proclaimed Tory member from Birmingham shared a post from the Rees-Mogg supporters’ page apparently complaining that Theresa May was too soft on “Islamic terrorism”. The post includes a picture of the prime minister wearing a hijab, with the message: “Sharia May.”

The post purportedly quotes May saying: “Britain benefits greatly from Islam,” adding in response: “Tell that to the families of over 100 innocent people who have been murdered on the streets of the UK in Islamic terror attacks.”

Another post she shared from the group read: “Why do Muslims insist on moving to non-Muslim countries and then complain that they find OUR way of life offensive. Why not remain in a MUSLIM country where their way of life is the norm?”

Photograph: Facebook

A third self-proclaimed Tory member from Plymouth wrote in response to an article about a Muslim pressure group calling on Germany to ban alcohol to prevent sexual violence: “Time to send them all back.” In another post in January, he railed against an “Islamic advert” on Facebook that he found “offensive”. He also shared a meme aimed at migrants which stated: “If you don’t like it, tough. Go back to Suckistan and change there.”

The fourth claimed Tory member implied “most” Muslims sexually assault young women in a post on the Rees-Mogg supporters’ Facebook page.

A different user shared a picture of dozens of Asian men convicted in grooming gang trials, writing sarcastically: “Police report: Not all Muslims sexually assault young women.” The suspected Tory member replied: “Just most do.”

A fifth self-proclaimed Tory member from Chichester, West Sussex, branded Ethiopia – where the second largest religion is Islam – a “primitive country with an equally primitive culture” as he shared an article on his Facebook page about the tragic death of 157 people on an airliner that crashed. After being challenged by a friend about his inflammatory comments, he responded: “Its [sic] a madhouse continent with only one civilised country & they are going about trashing that as I type.”

A spokesman for the Conservatives said: “Discrimination or abuse of any kind is wrong. When Conservative campaign headquarters has been made aware of the small number of such cases, we have acted swiftly, suspending or expelling members involved and launching immediate investigations, in sharp contrast to other parties. Our complaints process is rightly a confidential one.”