(fixes syntax of word in paragraph 5)
* ISIL insurgents suspend battles in most of Syria
* Photos show insurgents moving weapons from Iraq
BEIRUT, June 13 (Reuters) - The Syria branch of the Islamic State in Iraq and the Levant (ISIL) has put fighting on hold in Syria while it brings in weapons seized inside neighbouring Iraq, a monitoring group that tracks the violence said on Friday.
ISIL, a Sunni Islamist splinter of al Qaeda, has battled rival rebel groups in Syria for months and clashed occasionally with President Bashar al-Assad's forces.
But its fighters appear to hold back in Syria this week, especially in their eastern stronghold near the Iraqi border, while their Iraqi wing was making rapid military gains.
Rami Abdulrahman, head of the Syrian Observatory for Human Rights, said that ISIL may have negotiated a truce with rival rebel brigades in Syria, although it was still laying siege to parts of the eastern city of Deir al-Zor, where Assad's forces and al Qaeda-affiliated Nusra Front rebels are also dug in.
"(ISIL) has not been fighting for four days. We don't know why exactly. There is only some fighting northeast of Aleppo," Abdulrahman told Reuters by telephone.
Clashes between other rebel groups and government forces continued across Syria's civil war fronts, he said.
He said that ISIL, Sunni Islamists who have surged out of north Iraq to menace Baghdad and want to establish their own medieval-style state spanning Iraq and Syria, have moved weapons into eastern Syria.
"Our people saw weapons on the road in Syria," he said.
Photos posted on social media by ISIL supporters also appear to show military equipment, including American Humvee patrol cars, being moved.
Reuters cannot confirm they were taken into Syria but the supporters say they were driven across the frontier.
Matthew Henman, Head of IHS Jane's Terrorism and Insurgency Centre, said in a report that ISIL's capture of Iraqi territory along the Syrian border will give the group greater freedom of movement of men and materiel across the two countries.
"Light and heavy weaponry, military vehicles, and money seized by ISIL during the capture of (Iraq's) Mosul will be moved into desert areas of eastern Syria, which ISIL has been using as a staging ground for attacks," he said.
ISIL gained more ground in Iraq overnight, moving into two towns in the eastern province of Diyala, while U.S. President Barack Obama considered military strikes to halt their lightning advance.
Syria's civil war started with pro-democracy street rallies in 2011 but turned into an armed insurgency after a military crackdown on civilian protesters. Hardline factions like ISIL have gathered strength in the conflict, which has killed 160,000 people and displaced millions of people. (Reporting by Oliver Holmes; Editing by Mark Heinrich)