A Kurdish leader in Kobane told Reuters news agency IS militants had entered parts of the city amid heavy fighting.
The US military said its latest strikes had destroyed IS positions, but that Kobane "could be taken" by the group.
Seizing the town would give the IS jihadists full control of a long stretch of the Syrian-Turkish border.
The US also appeared to be at odds with allies over a Turkish idea to create a buffer zone or safe haven along the border.
Three weeks of fighting over Kobane has cost the lives of 400 people, and forced more than 160,000 Syrians to flee across the border to Turkey.
Asya Abdullah, a co-leader of the Kurdish Democratic Union Party representing Syrian Kurds in Kobane, said: "Tonight [Islamic State] has entered two districts with heavy weapons, including tanks. Civilians may have died because there are very intense clashes."
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