The Prime Minister says the term gives false credibility to the “poisonous death cult” which is “seducing” young Britons to fight for it in Syria and Iraq.
Speaking on BBC Radio 4’s Today Programme, Cameron said: “I wish the BBC would stop calling it ‘Islamic State’ because it is not an Islamic State.
“What it is is an appalling barbarous regime that is a perversion of the religion of Islam and many Muslims listening to this programme will recoil every time they hear the words.
“’So-called’ or Isil is better.” [Isil is the abbreviation of the self-proclaimed Islamic State of Iraq and the Levant]
On Monday BBC Political Correspondent Tim Reid tweeted: “PM agrees that Islamic State should not be used; says he raised the issue with the BBC this morning.”
This was communicated to Rowling via Stephen Daisley on Twitter, who wrote: “Tell me I’m not the only one uncomfortable with the Prime Minister seeking to dictate BBC editorial policy.”
Rowling replied in the affirmative: “You're not the only one uncomfortable with the Prime Minister seeking to dictate BBC editorial policy.”
A BBC spokesman told Huffington Post UK: "No one listening to our reporting could be in any doubt what kind of organisation this is. We call the group by the name it uses itself, and regularly review our approach.
"We also use additional descriptions to help make it clear we are referring to the group as they refer to themselves, such as 'so-called Islamic State'."
Cameron’s rhetoric comes in the wake of a deadly terror attack at a tourist holiday resort in Tunisia on Friday.
At least 18 Britons were among 39 holidaymakers killed in the Tunisian beach massacre, but the toll may well rise.
Isis has claimed it is behind the attacks and has reportedly identified Kalashnikov-wielding attacker Seifeddine Rezgui by his jihadi pseudonym Abu Yahya al-Qayrawani.
The 23-year-old Tunisian aviation student disguised himself as a tourist and began firing at holidaymakers on a beach using the gun he had hidden in a beach umbrella.
Some 39 other people were also wounded in the attack, including 21 who have already left hospital. Of the wounded, 25 were British.
The worst such attack in Tunisia's history came on the same day a man was found decapitated after an attack by suspected Islamic extremists on a French factory and a Shiite mosque in Kuwait was bombed, killing at least 25 people.