The Islamic State of Iraq and the Levant (ISIL) have launched a fresh bid to take over the Syria-Iraq border area and set up a state run by their interpretation of Islamic law, rebels, activists and a monitoring group say.

"Their goal is to link together the two areas (Syria, Iraq) to set up their state and then to continue spreading," said activist and citizen journalist Abdel Salam Hussein.

Speaking from Albu Kamal on the Iraq border, Hussein said ISIL is fighting to defeat al-Nusra Front, al-Qaeda's Syria affiliate, and control the eastern, energy-rich province of Deir Ezzor bordering Iraq.

"ISIL are trying to end al-Nusra Front's power in the area, and if they do they will take over" the whole province, he said.

ISIL's long-time ambition of creating an area under its control stretching across Syria and Iraq was undermined by a significant January offensive against it by rival rebel groups.

The campaign cornered ISIL fighters in Raqqa province, its stronghold in northern Syria.

Once welcomed into the rebellion against President Bashar al-Assad, ISIL's desire to govern unilaterally and their implementation of strict, often violent, punishments against civilians and rival fights has sparked the wrath of much of Syria's opposition, including former ally al-Nusra.

ISIL has its roots from al-Qaeda in Iraq, but it split from the network after overall al-Qaeda chief Ayman al-Zawahiri ordered it to stop fighting al-Nusra. In February ISIL withdrew from most of Deir Ezzor after pitched battles with al-Nusra and other rebel factions, said rebel spokesperson Omar Abu Layla.

Abu Layla says, however, that since then ISIL has deployed "3,000 fighters from Raqqa to Deir Ezzor", Abu Layla told AFP. "Most of them are foreigners, including Europeans, Tunisians and Saudis," he said.

"ISIL have orders from their leader Abu Bakr al-Baghdadi to focus on Deir Ezzor, to take it over. It's their main gateway to Iraq."

'Oil, money, weapons'

Violence is escalating in Deir Ezzor with daily battles pitting ISIL rebels against al-Nusra fighters, which has led to increasing incidents of car bombings, according to activists and the British-based Syrian Observatory for Human Rights group.

12 people, including three children, were killed in a car bomb attack on 16 May by ISIL, the Observatory said and, according to its director Rami Abdel Rahman, ISIL are expanding.

"They are pressing their bid by pushing tribes to swear oaths of loyalty to them, and by fighting rival factions in an attempt to ensure they emerge the strongest," he said. "ISIL have oil, money and weapons," he added.

Over the past year ISIL fighters have seized regime weapons depots even after they were captured in joint battles with other groups, said Abdel Rahman. Both the Observatory and activist Abdel Salam Hussein say ISIL now holds sway in much of the area east of the Euphrates river in Deir Ezzor province.

Hussein said the tribal nature of the area means the war there is more over oil and loyalty than ideology. He also said some rebel commanders in Albu Kamal, a key crossing point between Iraq and Syria still beyond ISIL control, "have sworn oaths of loyalty to ISIL".

Hussein says anti-ISIL rebels are fighting back, but that they have suffered heavy losses. "And with all the oil money coming in to Deir Ezzor, ISIL is able to keep its ammunition supplies well stocked," he added.

The group has distributed food to families affected by the fighting, in an attempt to gain support in an area impoverished by decades of marginalisation and three years of conflict and displacement.

"The other day they were giving out fruit to families. It's a tactic to win support," Hussein said.

But rebel spokesman Abu Layla, who opposes both ISIL and the Assad regime, said he believes ISIL has no future in Deir Ezzor.

"They want to use force to set up a brutal, extremist state that has nothing to do with Islam, and people reject that," Abu Leyla said. "Every day we are fighting ISIL and the regime, without a single bullet or dollar of support from the outside world," he added.

"They can never claim real, grassroots support. Nobody in Syria wants ISIL."