"IS fighters have seized at least 21 villages around Kobane," said Syrian Observatory for Human Rights head Rami Abdel Rahman, using the Kurdish name for Ain al-Arab.
"The IS is using heavy weaponry, its artillery and tanks," he said, adding that thousands of Kurdish fighters defending the town on the Turkish border were being encircled in a "pincer movement".
Kobane is Syria's third largest Kurdish town after Qamishli and Afrin. Its capture would allow the jihadists to control a long stretch of the Syrian-Turkish border.
Speaking to AFP via the Internet, an activist in Kobane said that apart from the villages seized by the jihadists, others have also been abandoned by residents fearful of the IS advance.
"If the situation doesn't change, it is very possible that (the 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 has cut off water and electricity supplies to the city.
Ali said Turkish authorities were blocking the only safe way out, into Turkey.
"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.
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The Syrian opposition National Coalition, meanwhile, warned of "the danger of a massacre of civilians" in the Kurdish areas.
Abdel Rahman said the latest IS offensive was larger than a July assault that was repelled by the Kurds backed by hundreds of fellow Kurdish fighters who crossed from Turkey.
In the thick of Syria's anti-regime uprising, the Kurds have established a semi-autonomous status in the Kurdish-inhabited regions of the country's northeast, clashing repeatedly with the IS to defend their territory since the jihadists made their entry into the conflict in the spring of 2013.
Anti-IS raids kill civilians
Elsewhere, at least 17 civilians were killed in Syrian regime air strikes on the town of Al-Bab, located in the northern province of Aleppo, said the Observatory.
Though Al-Bab is under IS control, all the dead were civilians, Abdel Rahman said.
The Assad regime has stepped up its campaign against IS-held areas, carrying out near-daily air raids. But activists say most of the casualties have been civilians.
Syria's war has killed more than 191,000 people since March 2011 and forced nearly half the country's population out of their homes.