In a video released Sunday, IS said it beheaded 21 Egyptian Christians on a Libyan beach, in a likely bid to strike fear and show the Sunni extremists' reach now stretches beyond its Iraqi and Syrian strongholds.
It comes three weeks after IS opened a new front on Western targets in Libya when it claimed an attack on the luxurious Corinthia hotel in central Tripoli that killed nine people, including five foreigners.
Islamist militants have thrived in Libya since Kadhafi was toppled and killed in the NATO-backed 2011 uprising, with authorities struggling to contain dozens of militant groups with diverse motivations and ideologies.
Amid the unprecedented uncertainty in the oil-rich North African nation, two main armed groups are vying for power.
The first is led by Khalifa Haftar, a former general who is backed by Libya's internationally recognised government and whose forces are fighting to drive Islamist fighters out of the country's east.
The other is Fajr Libya (Libya Dawn), an Islamist-led coalition that emerged from the western city of Misrata last summer to seize control of the capital and install its own government and parliament.
While it has regularly denounced "terrorism", Fajr Libya maintains links with the radical Ansar al-Sharia but does not recognise the Islamic State group's presence in Libya.
Its parliament, the General National Congress, has so far declined to confirm that the beheading of 21 Egyptian Christians claimed by IS took place in Libya.
But a spokesman for Haftar's forces has said that "the Libyan army has engaged in fierce battles against IS".
"There are sleeper cells in every town who liaise directly with (IS leader Abu Bakr) al-Baghdadi," Colonel Ahmed al-Mesmari told AFP.
"And there will be other terrorist operations against Libyans and foreigners who live in Libya," he said, appealing for support from the international community.
Signup to our newsletter and follow us on Facebook and Twitter!
Romain Caillet, an expert on jihadists, said that IS killed the 21 Egyptians to show that "its Libyan branch has now expanded and is the strongest outside of Iraqi and Syrian territory".
The rise of IS in Libya has heightened concerns in the region, including Egypt and Tunisia to its east and west, and Niger and Chad, southern neighbours who insist on the need for international intervention.
Across the Mediterranean, Italy is struggling to cope with an influx of migrants who set off for its shores from Libya, less than 300 kilometres (200 miles) away.
Rome on Monday ruled out military intervention in Libya in the short term, despite its defence minister talking of providing more than 5,000 men for a multinational intervention force which it would lead.
"Italy, whose coastline is very close to Libya, is most concerned by this threat," said analyst Ahmed Mohamed Nouh, explaining the talk of intervention.
"Europe understands that for it the problem hasn't come from Syria or Iraq, but from Libya which is very close to its shores."
An Arab diplomat formerly based in Tripoli said any military intervention in Libya would be difficult because of the complex situation on the ground.
"This would be rejected by Fajr Libya which has shady links with moderate Islamist groups and also radicals," said the diplomat who spoke on condition of anonymity.
"This will greatly reduce the chances of success of any coalition, even if it is mandated by the United Nations."
But another analyst, Mohamed el-Jareh, said the problem was no longer one for Libyans alone.
"At this stage, Libyans can no longer decide who can intervene in Libya, and how. Libya is no longer a Libyan problem," he said.