Capture of the Mosul Dam after an offensive of barely 24 hours could give the Sunni militants the ability to flood major Iraqi cities, sharply raising the stakes in their bid to topple Prime Minister Nuri al Maliki's Shi'ite-led government.
Isis, which sees Iraq's majority Shi'ites as apostates who deserve to be killed, also seized the Ain Zalah oil field, adding to four others already under their control, and three towns.
Isis fighters have also been involved in violent exchanges with Lebanese armed forces around a border town in a push to dislodge the biggest incursion by militants into Lebanon since Syria's civil war began.
At least ten Lebanese soldiers have died in the fighting, which erupted after Islamist gunmen seized a local police station on Saturday in response to the arrest of their commander, security officials said.
An unknown number of militants and civilians have also been killed, and security sources say at least 16 members of Lebanon's security forces have been taken captive.
The gunmen in Arsal include fighters linked to the Islamic State (Isis), the al Qaeda offshoot that has seized territory in Syria and Iraq, as well as Syria's al Qaeda branch, the Nusra Front.
Residents said many of the tens of thousands of Syrian refugees who had taken shelter in the hills around Arsal had abandoned their camps and were sleeping in the town's streets to escape bombardment. Fires had broken out in some camps.
"They're shelling from all directions," said Qassem al Zein, a doctor at the field hospital in Arsal, adding that the hospital had recorded ten civilians killed so far.
The confrontation in Arsal has been the biggest direct clash between Lebanon's army and rebels fighting to overthrow President Assad.