The Islamic State used car bombs and mortars to attack Kurdish fighters in the town.
The IS, which control much of northern Syria and Iraq, fired over 44 mortars at parts of Kobani controlled by Kurds. Some of the mortars landed inside the border of Turkey.
A battle of over a month has gone on for control of Kobani with both the Islamic State and Kurdish taking and losing momentum.
Kurds warned a week ago that the town would fall shortly to IS if the coalition, led by the U.S. did not increase air strikes, which it did.
The coalition has bombed the Islamic State inside Iraq since early August and extended its campaign into Syria last month after the militant extremist group made huge gains territorially.
Raids on IS around the town of Kobani were stepped up as the fate of this town is seen as an important test for the campaign of Barack Obama the President of the United States.
Turkey, a member of NATO, whose forces have fanned out along its border with Syria that overlooks Kobani, has become a reluctant coalition member, insisting the coalition should confront Syria President Bashar al-Assad as well to end the ongoing civil war that started in March of 2011.
Two car bombs set off by the Islamic State hit positions held by the Kurds on Saturday night. On Sunday, black smoke towered high above Kobani.
A fighter from the unit of females for the Kurdish militia in Syria said the Kurdish fighters detonated the car bombs prior to them reaching their targets.
She added that fighting went on Saturday night across all of Kobani and on Sunday morning, the fighting continued.
Sources close to the battle said 70 fighters from the Islamic State had been killed in the last two days.
Other sources said the Kurds had executed two captives from the Islamic State.
Executions have also been used by the IS during their entire campaign in Iraq and Syria. They have killed hundreds of civilians and fighters who opposed their cause.