“They want to carve out a jihadi state or a jihadi territory and obviously anything above that is gravy, like overthrowing the Assad regime,” said Bruce Hoffman, director of the Center for Security Studies at Georgetown University. “I don’t think they have ambitions of taking over the entire country, although they’d be happy to.”

While the Syrian rebels initially welcomed the group as a powerful ally in the civil war against President Bashar al-Assad, many now resent it for putting its international jihadi agenda ahead of the fight to topple the government. Antigovernment activists say they detest the group’s brutality and imposition of strict social codes, and even other Islamist rebels say the struggle’s focus should remain on leadership change.

The tensions have set off frequent fighting between rebel groups that has undermined the effort to combat the government and could complicate efforts to dispose of Syria’s chemical weapons. An advance team from the Organization for the Prohibition of Chemical Weapons arrived in Damascus on Tuesday to discuss with Syrian officials the logistics of destroying the country’s chemical arsenal. Officials from the group said keeping its personnel safe during a raging civil war would be extremely difficult.

The rise of extremist groups has exacerbated Syria’s instability. ISIS has attacked rebel bases to capture supplies, and routed rebel groups last month to seize control of Azaz, a strategic city near the Turkish border, leading to a tense cease-fire. Last week, Qaeda fighters tried to storm a village in Idlib Province to kidnap some rebels, leaving 20 dead from both sides, including the jihadis’ Libyan commander.

“We want to keep Syria together as a country of freedom and equality,” a leader in an Islamist rebel group opposed to ISIS, called Suqour al-Sham, who gave his name as Abu Bashir, said via Skype. “They want to form an Islamic state that comes together with Iraq.”

In an audio statement released online late Monday, a Qaeda spokesman defended the group, saying its contributions to the anti-Assad fight had been underappreciated and denying that it had started fights with rebel groups.

“Those who aspire to sideline the state are many because of incorrect beliefs and doctrines,” said the spokesman, Abu Mohammed al-Adnani al-Shami. “They are greedy for power and for the worthless things of this world.”

Analysts say the group is a revival and extension of Al Qaeda in Iraq, whose sectarian-fueled insurgency pushed that country to the brink of civil war in 2006 and 2007, before the group suffered major defeats at the hands of tribal fighters and American troops.

In Syria, however, the group has found the vast territories that have fallen into rebel hands near Syria’s northern and eastern borders as an ideal environment to regroup and advance its agenda.

The area is stateless, covered by a weak patchwork of local councils and rebel groups struggling to administer their towns and often competing with one another for resources. This gives the group a wide area to work in with no immediate enemies. The porousness of the Iraqi and Turkish borders also makes it easy for the group to bring in supplies and fighters.

Brian Fishman, a former director of research at the Combating Terrorism Center at West Point and now a fellow at the New America Foundation, said those factors gave Al Qaeda a more favorable environment in Syria than it ever had in Iraq.

“The conditions in Syria will be ripe for ISIS for quite some time,” he said.

The group is headed by an Iraqi named Abu Bakr al-Baghdadi. Its fighters hail from across the Arab world, Chechnya and other parts of Europe and are commanded by local emirs to whom they pledge obedience, according to rebels in contact with the group.

While ISIS fighters have lined up alongside rebels against the government, rebels said the group appears to focus on areas already wrested from Mr. Assad, even if that means displacing rebels

“The idea is that they are trying to control the areas that are already liberated,” said Thaer Shaib, a rebel fighter from Idlib Province. “We go to the front, we liberate areas and leave a few fighters behind in order to advance, and then they come and hit us in the back.”

Throughout the scattered areas the foreign jihadis control along Syria’s northern border, they have banned smoking in public and attacked Kurdish villages, some of which had truces with the rebels.

In Raqqa, the only regional capital to fall under full rebel control, ISIS has set up bases in government buildings, publicly executed members of the minority Alawite sect, to which Mr. Assad belongs, and detained activists who have protested against it.

“They control through fear, by holding public executions, walking around in masks, showing their weapons, and killing and kidnapping anyone who stands against them or their acts,” said an activist in Raqqa who declined to give his name for fear that extremists would hunt him down.

Although the group sometimes cooperates in battle, ISIS is separate from the first Qaeda group to emerge in Syria, the Nusra Front, whose leader rejected a proposed merger this year.

Since then, foreign fighters have flocked to ISIS, while the Nusra Front has been more clearly accepted by mainline rebels for keeping its focus on the fight against Mr. Assad.

An American official said that ISIS was smaller than Nusra and a “tiny” part of the armed opposition, but that the group appears to be growing by attracting some of the most extreme foreign fighters.

The official also said that the group’s fights with other rebel brigades could harm it if the clashes lead to a popular reaction against it.

Last week, 10 Islamist brigades signed a statement with the Nusra Front calling for an Islamic state and rejecting the exile opposition, the Syrian National Coalition. Members of the groups that signed said the statement was also intended to project unity among Islamic rebel brigades that do not share ISIS’s agenda.

ISIS makes its vision for Syria clear in videos it releases on militant Web sites, showing its fighters seeking to help the poor, spread their strict interpretation of Islam and kill those they consider infidels.

One video about a recent ISIS offensive in the central province of Hama showed a commander laying out battle plans to a group of fighters with images from Google Earth projected on a wall.

“We have to give them a lesson that their plans will fail,” said the unidentified commander said, who had a long beard and shoulder-length hair. “Syria will be nothing but an Islamic caliphate, God willing.”

Later footage showed scores of well-armed fighters, some speaking broken Arabic, riding off to battle and singing, “For slaughter we came for you, O Alawites,” a reference to Mr. Assad’s sect.

The group does not hide its cross-border operations or its brutality toward those it deems enemies. In another video, a group of fighters stops three truck drivers on a highway believed to be across the Iraqi border and asks them how many times they bow during dawn prayer, an easy question for a pious Muslim.

The men, who are Alawites, guess incorrectly. The fighters pronounce them infidels, make them kneel by the side of the road and gun them down. Then one fighter throws a Molotov cocktail into one of the trucks, setting it on fire.

Karam Shoumali contributed reporting from Istanbul, Eric Schmitt from Washington, and an employee of The New York Times from Beirut.