No IS fighters were yet inside Kobane, according to Idris Nahsen, deputy foreign minister of the region, who spoke to AFP by phone from the besieged town.
"They are one kilometer away in some places and two or three kilometers in other places," he added.
There have been further US-led air strikes aimed at stopping the Terrorists but Nahsen said they would not be enough by themselves to stop the advance of IS.
"They are not enough to defeat terrorist groups on the ground. They (the US-led coalition) have to help with ammunition and weaponry.
"The strikes are helping but we need heavy weaponry, armored vehicles, cannons, rockets. And air strikes need to be more effective," he told AFP.
Kurdish fighters have been battling the advance of IS militants around Kobane for the last two weeks. Some 186,000 refugees have fled to Turkey since the fighting began.
IS fighters seized part of a strategic hill overlooking the town of Kobane late on Saturday, a monitor said, but their progress was slowed by new strikes from the coalition of Washington and Arab allies.
"IS succeeded on Saturday night in taking the southern part of the Mishtenur hill," the Observatory's Rami Abdel Rahman told AFP.
If the Terrorist seize the hilltop, he said, "the whole town of Kobane will be in their sights and it will be easier to take".
In a statement, US Central Command said the US military carried out 3 air strikes in Syria on Saturday, while fighter jets, bombers and helicopters were used in 6 assaults against IS positions in Iraq on Sunday.
The number of dead in fighting between Kurdish fighters and IS Terrorists on Sunday was not known, but the Observatory, which relies on a network of local sources, said at least 33 IS fighters and 23 of the town's Kurdish defenders were killed on Saturday.