More than half of Conservative members questioned for a new poll believe Islam is a threat to British life.
YouGov was commissioned by Channel 4's Dispatches programme to carry out a survey among the members who will decide whether Jeremy Hunt or Boris Johnson becomes the next Tory leader.
Of the 892 members questioned, 56% said Islam threatened British values.
The party's chairman Brandon Lewis said the poll was "hardly representative" and questioned the methodology used.
In a series of tweets, he suggested there was a "danger" in relying on the responses of fewer than 900 people when the party membership was about 180,000.
The Conservative Party has been criticised for its response to allegations of Islamophobia among party members,
Its former chair Sayeeda Warsi, one of the party's most outspoken critics, said the findings of the poll were "disturbing" and pointed to a "lurch to the right" at grass-roots level.
The Equality and Human Rights Commission is currently considering a formal complaint submitted by the Muslim Council of Britain, which details examples of Islamophobic comments made by party members and activists.
Channel 4's Dispatches, broadcast on Monday night, highlighted further comments made on social media by people claiming to be Conservative members.
A party spokesman said: "Those people making these posts that we have found to be members of the party have been suspended pending investigation.
"Discrimination or abuse of any kind is wrong and will not be tolerated."
During the Conservative leadership campaign, both candidates have condemned all forms of racism and discrimination.
Jeremy Hunt has committed to holding a specific independent inquiry into the extent of Islamophobia in the Conservative Party if he becomes leader.
Boris Johnson told the Conservative Home website he would hold a general, independent investigation into all types of prejudice and discrimination.
Among the other findings of the YouGov poll, 58% of respondents thought the death penalty should be allowed for certain crimes, while 46% thought concerns about climate change were exaggerated.