The capture of Ain Al-Arab -- Syria's third largest Kurdish town, known to the Kurds as Kobane -- would give IS control of a big swathe of Syria's northern border with Turkey.
"IS fighters have seized at least 21 villages around Kobane," the Syrian Observatory for Human Rights said.
"IS is using heavy weaponry, its artillery and tanks," said Observatory director Rami Abdel Rahman, adding that thousands of Kurdish fighters defending the enclave were being encircled in a pincer movement.
"If the situation doesn't change, it is very possible that (IS) will enter the city," said Jan Ali, using a pseudonym to protect his identity.
"We are seeing the signs of a humanitarian crisis in Kobane," he said, adding that IS had cut off power and water.
Ali said Turkish authorities were blocking the only safe way out, over the border.
"People from the villages have fled to the city... Some are trying to cross into Turkey but the Turkish authorities are not allowing them," he said.
The area is one of three Kurdish-majority districts where Kurdish leaders have declared self-rule, taking advantage of the withdrawal of government forces in the face of a three-and-a-half-year-old uprising.
Abdel Rahman said the latest IS offensive was bigger than one in July that was repelled by Kurdish fighters backed by hundreds of fellow Kurds from across the border in Turkey.
Further west, Syrian government air strikes on the IS-controlled town of Al-Bab killed at least 26 civilians, the Observatory said.
More than 191,000 people have been killed in Syria since the uprising against the rule of President Bashar al-Assad erupted in March 2011.
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