ALGIERS/CAIRO (REUTERS) - The images match the worst of Islamic State in Iraq and Syria's atrocities: black-clad fighters and an English-speaking militant taunt the West before slaughtering their victims in orange jumpsuits on a Libyan beach.

Their masked leader turns to the Mediterranean and points a bloodied knife towards Europe, declaring, "We will conquer Rome, God willing."

The execution of 21 Egyptian Christians by militants in Libya proclaiming allegiance to Islamic State was an announcement that the group, also known as ISIS or ISIL, has spread from Syria and Iraq to Libya. Militants have profited from chaos to claim a North African outpost a boat ride away from Italy's coast.

International reaction came swiftly. Egyptian jets pounded suspected militant sites in Libya, and Paris joined Cairo in calling for UN action to halt the militants' spread.

Libya appears to be ISIS' most successful move yet beyond its Middle East heartland, likely attracting more recruits and increasing Western fears of a new North African base for militant fighters.

Yet, even as they thrive in Libya's unrest, ISIS sympathisers must contend with rivalries and factional infighting that make securing the sort of territorial gains that ISIS has made in Iraq and Syria more complicated.

"The statement in Libya is more a statement of defiance," said Hassan Hassan, co-author of a book on ISIS. "By killing Christian civilians, they were delivering a message that they're expanding."

The rise of ISIS comes as no surprise. Libya has descended into factional fighting, leaving the country almost lawless nearly four years after Muammar Gaddafi's fall.

Two competing governments backed by militia brigades are scrambling for control. Diplomats have fled, Tripoli's airport is a bombed-out shell and oil flow is a trickle as combatants trade rockets and air strikes.

Libya's ISIS sympathisers have used social media to display shows of strength, parades of armed men and appeals to implement syariah law in the eastern city of Derna, a stronghold of Islamist militancy.

But this year, ISIS militants in Libya have escalated operations. Last month, they claimed an assault on the Tripoli Corinthia hotel, killing nine people.

Islamic State gunmen also attacked Libya's Al-Mabrook oilfield, where France's Total owns a stake. Some victims were beheaded.

A US government source said US officials do not yet know how many attacks by Islamic State sympathisers are directly tied to the central organisation or are just "copycat" claims.

But analysts said the Egyptian killings, their video release via an official ISIS outlet, exerpts from an ISIS magazine on the hostages and the executions themselves suggested ties with ISIS command.

TRAINING CAMPS

In December, General David Rodriguez, head of the US Africa Command, said a couple of hundred militants were in training camps in eastern Libya that were likely to send fighters to Syria.

Now foreigners are being killed fighting for Islamist groups in Libya. Tunisian newspapers carry death notices of militants who have died not only in Syria or Iraq, but also in Libyan cities like Benghazi.

For Egypt, the rise of Islamic State just over its border is worrying. Egyptians officials see ties between Libyan Islamists and militants in the Sinai.

"What you have is a chaotic country where Islamic State and other militant groups are untouchable, on your border," a senior Egyptian security source told Reuters.

"Our goal is not to contain terrorists with air strikes, our goal is to eradicate terrorism in Libya."

Libya is also host to Ansar al Sharia, blamed by Washington for an attack on the US consulate in Benghazi where the US ambassador died, and Al-Qaeda-linked groups as well as smaller Islamist rivals whose motives are more local than global.

That may limit the ability of ISIS to consolidate in Libya.

"You will end up with sporadic hits like the attack on the Corinthia," said Geoff Porter, North Africa specialist and assistant professor at the Combating Terrorism Centre at West Point. "That is different from holding territory, collecting taxes, providing state services."

NEW ISLAMIST BASE?

But in Derna, a conservative city where Islamist hardliners once resisted Gaddafi, residents say ISIS supporters are exerting more influence, cracking down on public smoking and shisha pipe cafes.

ISIS is adept at propaganda that often exaggerates its victories, and social media accounts are hard to verify. But in one image, ISIS militants parade in a long column of Toyota jeeps near Sirte. Another image in Derna shows ISIS supporters driving white SUVs with "Islamic Police" emblazoned in black.

Residents and activists in Derna were wary of talking about militants, who have carried out assassinations there. They said a Yemeni, believed to be named Abu El-Bara El-Azadi, arrived in Derna late last year as a representative of Islamic State.

ISIS has gathered local support in Derna through the Libyan group, Shura Council of Islamic Youth. Even there in its main Libyan base, analysts and residents say, it is not fully in control and faces resistance from competing Islamist groups.

But ISIS may be "poaching" from other movements, especially among younger fighters drawn to its powerful message and high profile, said Thomas Joscelyn, who monitors militant movements for The Long War Journal.

Several residents said ISIS held the Egyptian Christian hostages in Derna, but they saw them being transported out of the city about two weeks ago. A camera crew was with them.

Residents said after the video was released, ISIS members increased security and some leaders went underground.

"There now is a seed group of battle-hardened men who have fought with ISIS," said Harleen Gambhir at the Institute for the Study of War.

"ISIS is exerting control over Derna... and it now has operating space to plan larger attacks."