The Conservatives are under pressure to suspend two serving councillors who made anti-Islam comments, including one alleging all 11-year-old girls should be frightened of Islam.

Mohammed Amin, chairman of the Conservative Muslim Forum, said he had “lost confidence in the Conservative party’s disciplinary processes when the promotion of anti-Muslim hatred is the subject,” after the party said it was investigating John Moss and Nick Coultish.

The Muslim Council of Britain (MCB) has demanded the UK’s human rights watchdog launches an inquiry into Islamophobia in the Conservative party.

Labour also criticised the party for “failing to take swift action in suspending councillors who have spouted clear Islamophobic comments”.

Naz Shah, the shadow equalities minister, said: “Despite the Conservative party denying an independent inquiry on the matter, failing to suspend councillors and even allowing those expressing such hate back into the party through the back door, there has been widespread neglect from the media to hold them to account for this issue.”

Faiza Shaheen, Labour’s candidate in Chingford, where one of the councillors sits, said Muslim residents were sharing the comments with horror on local social media groups.

Moss, a Tory councillor in Waltham Forest, said that “every 11-year-old girl” should be scared of Islam when responding to a tweet about Islamophobia, according to screengrabs posted by BuzzFeed. He also tweeted: “I reject Islam’s barbarism, its sexism, its racism, its homophobia,” and sent tweets to numerous prominent Muslims asking them to “denounce those bits of the Quran they don’t live by”.

Moss, the former chairman of Chingford and Woodford Green Conservatives, is a prominent local figure who has acted as an election agent in local ballots. He also stood as the parliamentary candidate in Hackney South in 2005.

Shaheen, the director of the Class thinktank, said Moss’s own ward contained a popular mosque. “I’m sickened to read these racist and Islamophobic tweets from a prominent local Conservative councillor,” she said. “That there is a mosque in John Moss’s ward makes these comments even more alarming. All forms of racism and religious intolerance have to be fought with all we have. Our diverse Chingford community deserves better.”

Moss told BuzzFeed that the context for his remarks about 11-year-old girls was female genital mutilation, though he admitted the practice was “not limited to the Muslim community and is not even commonplace within that community”. He said he had provided a full response to the party and would await the outcome of the investigation.

The Conservatives also said they would investigate East Riding Tory councillor Nick Coultish, who posted tweets apparently comparing the number of Muslims in the UK to the German bombing campaign during the second world war. “Britain withstood the Blitz and got up, had a cup of tea and got on with rebuilding the next day. We will stand against the tide of Islam,” he tweeted.

Coultish apologised for his comments in a Twitter post on an account that was later deleted. He called the BuzzFeed article misleading and said the comments were “off-the-cuff … at the time of a terrorist attack in the UK”. He said: “These comments were made before university and at a low-point for me, I was upset and grieving and trying to make sense of the lives lost.

“My comments were wholly reactionary and unthoughtful, I was referring to radical Islamic extremism, of course, not real Muslims who are peaceful and live with British Values. I was young, not yet involved in politics in a big way and naïve. I’m sorry for any confusion or any offence my historic tweets caused.”

The MCB filed a complaint of more than 20 pages to the Equality and Human Rights Commission (EHRC) on Tuesday, saying calls for the party to allow an independent inquiry had so far been largely ignored.

The party was also recently criticised for rejecting a definition of Islamophobia put forward following a parliamentary inquiry. The Conservatives have already suspended dozens of members for Islamophobic comments on social media, including some directed at the Tory leadership contender and home secretary Sajid Javid.