The strikes came a day after the extremists pushed into Kobane, seizing three districts in the city's east after fierce street battles with its Kurdish defenders.
Today, the fighting had spread to new areas in the south and west, a monitor said.
However with Kurdish People's Protection Units (YPG) fighters seeking to halt the IS advance, a Kurdish flag could still be seen flying from a roof in the centre of the town, the correspondent said.
The IS jihadists "are in the east side of the city. They are trying hard to capture the city. But there is resistance from YPG fighters which stopped their progress Monday and last night," he said.
The US-led coalition airstrikes, which continued in the night and the morning, are "helping but are not enough", he added, calling for arms and ammunition to be supplied to the Kurdish fighters.
He said the Kurds were in contact with both the US-led coalition and Turkey in search of more assistance.
