The attack came after a Kurdish female fighter blew herself up at an IS position on Sunday, using the jihadists' own tactic against them, the Syrian Observatory for Human Rights said.
IS militants attempted to storm the town from both east and west of a strategic hill to the south but Kurdish fighters repulsed the attack, said the Britain-based group, which has a wide network of sources inside Syria.
Fierce clashes raged through the night but abated on Monday morning, with sporadic IS mortar fire against the town, the group's director Rami Abdel Rahman said.
But so far, Kurdish fighters have managed to keep the jihadists out of the town, with the backing of some US-led air strikes.
IS has seized much of the area around Kobane, however, surrounding it from three sides and triggering an exodus of some 186,000 refugees into neighbouring Turkey.
The fighting killed at least 19 Kurdish fighters and 27 IS jihadists yesterday, the Observatory said.