Meanwhile, the jihadi group has been gaining popularity inside Jordan, mainly in the poorer towns of the south where disaffection at rising unemployment and government corruption has been translated into a growing support for Islamism.
Police have been kicked out of the southern town of Maan and, while it is unclear how many Jordanians support the Islamic State, thousands have travelled to Syria to join various rebel groups and could link up with forces hostile to King Abdullah on their return.
Since the early 1970s, long before the two countries signed a peace treaty in 1994, Israel has acted as a silent guarantor of the Kingdom's security, along with its traditional allies Britain and the United States. Back in the days of the Black September Palestinian terrorist organisation, the IDF mobilised forces to prevent a possible takeover of the country by the PLO and Syria. Nowadays, security co-operation comes mainly in the shape of intelligence-sharing. According to reports in the Western media, Israeli drones perform surveillance flights over the Syria-Jordan border to provide both the IDF and Jordan with up-to-date information.
The Islamic State's announcement this week that it was changing its name included a declaration that its fighters would "liberate Palestine".
For Israel, however, the organisation does not currently pose a direct threat. Despite recent efforts of Salafists to establish a toehold in the West Bank, the Israeli and Palestinian security forces there have not allowed them to establish themselves.
In the Gaza Strip, a number of small jihadi (not to be confused with Palestinian Islamic Jihad) factions are competing with Hamas and the more established Palestinian organisations. They have tried to carry out operations against Israeli and Egyptian targets.
Egyptian sources claim that Islamic State fighters are now also operating in Sinai. But they do not yet seem to be present in sufficient numbers to change the balance in that particular region. Meanwhile, all other players - Israel, Egypt and Hamas - have a joint interest in not allowing them to do so.
For Israel, the main implication of the rise of the Islamic State could be the return of a "moderate" alliance reaching from northern Iraq, where the Kurds are now exercising more independence, through Jordan to Egypt. It may even include Turkey which, for the first time, seems to be warming to the idea of Kurdish sovereignty.
On Sunday, Mr Netanyahu effectively became the first world leader to endorse Kurdish statehood. He said that Israel had to "support the aspirations of the Kurds for independence" since they were "a fighting nation which has proved political commitment and moderation and deserves independence".
