But the Salafists in the enclave tread a fine line to avoid conflict with Hamas, the Islamist movement which has ruled the strip for a decade but does not share IS's world view.
Leaders of the Salafists, who are adherents of a strict Sunni interpretation of Islam, claim to have 3,000 fighters in Gaza.
While the figure is impossible to verify, experts see an increasing use of IS-style rhetoric to attract support.
"Some groups use the Islamic State label and claim to have adopted jihadist ideology to attract teenagers who have lost all hope," said Assaad Abu Charakh, a professor at Al-Azhar University in Gaza.
Last week saw the heaviest cross-border clashes between Israeli forces and Hamas and other militant groups since 2014, raising fears of a return to hostilities, though calm has since returned.
Israel has maintained a blockade on Gaza since 2006 aimed at containing Hamas, the Jewish state's arch enemy.
At almost 45 percent, the unemployment rate in the Gaza Strip is among the world's highest.
Hamas won the 2006 Palestinian parliamentary elections, but Israel and the international community refused to accept the results, demanding Hamas renounce violence, recognise Israel and respect agreements signed between Palestinian and Israeli leaders.
The party imposed its rule on Gaza a year later after a quasi-civil war.
Qassam Brigades defectors
But some members of the Ezzedine al-Qassam Brigades, Hamas' armed wing, argued elections were un-Islamic and defected to form Salafist groups.
Abu al-Ansari al-Ina, a leader of the "Young Salafist Fighters," one of the major jihadist groups in Gaza, is one such defector.
The priority, he argues, is the "fight against the Jews in Palestine, even if the strategic goal is the introduction of Islamic law in the world."
He says he is under surveillance and took precautions before meeting an AFP journalist.
Two hundred Gazans, including some of his movement, have crossed into Egypt to join the ranks of the Islamic State "despite Hamas' attempts to stop them," he says.
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Most used the tunnels that once linked Gaza to Egypt, while others took advantage of the occasional openings of the Rafah border crossing, the only of Gaza’s borders crossings not controlled by Israel.
The vast Sinai desert is gripped by an insurgency that Egypt regularly accuses Hamas of supporting.
Egypt's air force has destroyed a large number of the tunnels and established a buffer zone along the Gazan border.
Abu Sayyaf, military commander of another Salafi movement, insists Israel is the primary enemy.
"Our priority now is to strengthen the military capabilities of our fighters to kill the Jews, the enemies of God," he said.
"We do not want confrontation with Hamas," but "we will not hesitate to fight the infidels or anyone who stands in the way of our fighters."
Hamas security services reached an agreement last year with the jihadists after arresting about 100 of them: in exchange for their release, the groups committed to respect the truce with Israel and not to attack Palestinian or foreign institutions in Gaza.
Though limited, Salafi attacks endanger the ceasefire which Hamas is tactically keen to uphold.
Gazan groups have been firing rockets into Israel for years, with Israel retaliating by striking Hamas positions -- holding the militant group responsible for stability in the enclave.
Many fear the tensions could escalate into clashes between Hamas and jihadi groups if rocket attacks occur.
Salafi jihadists threatened Hamas in online videos, with some claiming the shelling of Qassam bases. "We met our commitments but Hamas did not, they again arrested some of our fighters," says Abu al-Ina.
Mahmoud Zahar, a top Hamas official, says the authorities "discuss and are trying to reason" with the imprisoned Salafists, but have no choice but to use force against aggressors.
A Salafist was killed last year by Hamas forces who had come to arrest him.
Some jihadists "were planning to kill their neighbours and relatives," Zahar said, provoking Hamas to step in to prevent "a huge explosion".
Asked about the IS links, Abu al-Ina al-Ansari says they merely consist of "an exchange of ideas but are not organisational".
"We agree with the clear message sent by the Islamic State to the miscreant West: 'Stop your attacks, we will stop our attacks'".