"ISIL fighters have seized at least 21 villages around Kobane," said Syrian Observatory for Human Rights head Rami Abdel Rahman.
"The ISIL 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 ISIL advance.
"If the situation doesn't change, it is very possible that (the ISIL) 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 ISIL 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.
The Syrian opposition National Coalition, meanwhile, warned of "the danger of a massacre of civilians" in the Kurdish areas.
Meanwhile, Ocalan Iso, deputy commander of Kurdish forces in Kobane, told Reuters the Kurds were seeking support from other groups including the Kurdistan Workers' Party (PKK) to fend off the advance by ISIL. Speaking via Skype, he said they wanted support 'in all military aspects.'
"We've lost touch with many of the residents living in the villages that ISIS (Islamic State) seized," Iso said.
He said the group was committing massacres and kidnapping women in the newly-seized areas. It was not possible to immediately verify his account.
For his part, Abdel Rahman said the latest ISIL 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 ISIL to defend their territory since the jihadists made their entry into the conflict in the spring of 2013.