The attacks came one after the other in the space of a few hours.

In France, a decapitated body covered in Arabic writing was found after an attacker rammed his car into a gas container, triggering an explosion. In Kuwait, a suicide bomber blew himself up in a packed Shi'ite mosque during Friday prayers, killing more than two dozen. And in Tunisia, at least 37 people died when a gunman opened fire at a popular tourist hotel.

There is no evidence the three attacks were deliberately coordinated. But coming so close together on the same day on three different continents, they underscored the far-reaching and fast-growing influence of Islamist group Islamic State, western politicians said.

The ultra-radical group, which has claimed direct responsibility for the Kuwait attack, clearly now poses a threat far beyond its heartland in Syria and Iraq.

It urged its followers this week to escalate attacks against Christians, as well as Shi'ite and Sunni Muslims fighting with a U.S.-led coalition.

On June 23, Islamic State spokesman Abu Muhammad al-Adnani urged jihadists to turn the holy month of Ramadan into a time of "calamity for the infidels ... Shi'ites and apostate Muslims".

"Be keen to conquer in this holy month and to become exposed to martyrdom."

The Pentagon was looking into "whether or not these various and far flung attacks were coordinated centrally or whether or not they were coincidental," spokesman Colonel Steve Warren said, noting Islamic State had claimed responsibility for one attack.

The US State Department said later there was no indication they were coordinated on a tactical level but were clearly all "terrorist attacks".

US Homeland Security Secretary Jeh Johnson said police should be vigilant and prepared, especially ahead of the US Independence Day holiday on July 4. Britain, which said at least five of its nationals were among those killed in Tunisia, summoned its emergency committee to discuss that attack and the one in France.

"This is a threat that faces all of us, these events that have taken place today in Tunisia and France, but they can happen anywhere - we all face this threat,"  Prime Minister David Cameron told reporters.

"JUST ACT"

Two sources familiar with the thinking of US intelligence agencies said that even if the attacks were not coordinated, they were likely to have been inspired by Islamic State's call to jihad or, possibly, the one year anniversary on Monday of the group's declaration of an Islamic caliphate in Syria and Iraq.

Adam Schiff, the top Democrat on the US House Permanent Select Committee on Intelligence, said the attacks made clear that Islamic State's "ability to inspire and radicalize followers is a global threat and no nation is beyond its insidious reach".

Ed Royce, Republican chairman of the US House of Representatives Foreign Affairs Committee, said the attacks showed that the ISIS threat was spreading well beyond Iraq and Syria and called for better regional coordination in the fight against the militants and more targeted air strikes.

"We must aggressively deny ISIS an area from which to unfurl their black banners of hate and death and plot their attacks," he said in a statement.

US Republicans have been extremely critical of President Barack Obama's response to the threat posed by Islamic State.

Peter Neumann, director of the International Centre for the Study of Radicalisation, based in London, also said it was unlikely the attacks were directly coordinated.

"I don't think that they talked to each other, knew of each other, or that there was a central command that told them to do that," he said. "There is zero evidence that they were coordinated."

At the same time, the French attack, which Neumann likened to other lone wolf attacks in the past year including in Sydney, Ottawa and Copenhagen, could have been inspired by Islamic State.

"In the case of the French attack, it's exactly the kind of attack that Islamic State wants people to do on their own without any prior consultation, coordination or whatever."

In September last year, Neumann said, the Islamic State spokesman urged followers not to "wait for us to tell you what to do. From now on you have permission to just strike wherever you want, kill infidels wherever you find them, do whatever is within your capability, just act."

While Islamic State has claimed direct responsibility for only the Kuwait attack, one Islamic State fighter told Reuters that in a general sense the assaults in both Kuwait and Tunisia had the blessing of the Islamic State caliphate.

"The speech of (IS spokesman Abu Muhammad) al-Adnani, may God protect him, he ordered soldiers and Amirs to make the month of Ramadan, the month of conquests and so it will be."