The Prime Minister – who calls the group ‘ISIL’ – said Muslims would ‘recoil’ at the phrase being used to justify the ‘perversion of a great religion’.
He insisted that the battle against extremists targeting Britons around the world can be won but will require ‘extraordinary resolve and patience’.
Gunman Seifeddine Rezgui targeted tourists at the Tunisian beach resort of El Kantaoui near Sousse on Friday morning, killing 38 people including up to 30 British tourists.
Mr Cameron urged Imams and Muslim leaders to continue to speak out against the terrorism carried out under a ‘perversion of a great religion’ and that extremism is a ‘gateway into terrorism’.
He criticised BBC presenter John Humphrys for referring to the group as Islamic State.
The extremists are variously known as Islamic State, Islamic State of Iraq and Syria (ISIS), Islamic State of Iraq and the Levant (ISIL) and DAESH, based the Arabic acronym.
During his interview on BBC Radio 4’s Today programme Mr Cameron referred to the group as ‘ISIL’.
‘I wish the BBC would stop calling it Islamic State because it’s not an Islamic State; what it is an appalling, barbarous regime,’ Mr Cameron said.
‘It is a perversion of the religion of Islam and many Muslims listening to this programme will recoil every time they hear the words ‘Islamic State’.
However, some people on social media pointed out that ISIL is an acronym which refers to ‘Islamic State’.
Mr Cameron repeated his criticism of the BBC for referring to the group as Islamic State: ;I think this is particularly offensive to many Muslims who see, as I see, not state but a barbaric regime of terrorism and oppression that takes delight in murder and oppressing women and murdering people because they are gay.
‘I personally think that using the term ISIL or ‘so-called’ would be better than what they currently do.
‘I don’t think we will move them all the way to Daesh so I think saying ISIL is better than using Islamic State because it is in my view neither Islamic nor a state.’