Councillor Judith Clementson, who represents Denmead, was suspended from the party after anti-racism group Hope Not Hate alleged she was behind a series of inflammatory tweets.
It comes after Portsmouth Conservative councillor Linda Symes was suspended for sharing posts described by political opponents as ‘undeniably racist’.
When asked about the tweets, Cllr Clementson did not deny or admit to running the account in question.
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She said: ‘I am not jumping on the MSM (mainstream media) bandwagon.
‘I am not denying or admitting it’s my handle.
‘I will not play the game.’
One of the tweets from the account @Clem205 with the name ‘Duffy Mac’ said Britain should ‘wake up or it will will be too late’ and ‘we will all be Muslim’.
Another added: ‘Unfortunately, its difficult to tell the “nice, peaceful” Muslims from the radicalised terrorist and the “nice, peaceful” ones probably know who they are and do nothing to stop them.’
When called a racist, the Twitter account replied: ‘Please don’t say that... I’m not racist and my Muslim friends will vouch for me on that score.
‘To call someone “racist” because they state fact is typical of our society today. It’s a means to discourage debate about reality by labelling those who are prepared to state truth.’
Caroline Horrill, leader of the Conservative group at Winchester City Council where Cllr Clementson serves, confirmed that she had been suspended from the Conservative party pending an completion of the investigation.
‘She is suspended from the Conservative party nationally, who are investigating her suspension.’
As a consequence of this, Cllr Clementson has no active part in the Conservative councillor group until this is resolved.
‘Cllr Clementson isn’t a member of any of our committees at this time,’ Cllr Horrill said.
‘We are in that period of waiting for the investigation to completed by central office.
‘The monitoring officer is aware she’s been investigated.
‘I’m not party to any of the investigations.’
In a report, Hope Not Hate said: ‘City councillor Judith Clementson uses the anonymous Twitter handle @Clem205 to post Islamophobic conspiracy theories about a “dangerous Muslim agenda for world domination”.’