The fought-over town was attacked on Thursday. Hundreds of people living there were reportedly massacred.
The focus of the fighting has now moved to Hassakeh, around 270 kilometers further east. It was also attacked on Thursday.
Officials say the Turkish and US governments have discussed the attack on Kobane and possible regional cooperation in a telephone call.
The UN estimates around 60 000 people fled the fighting in Kobane. An estimated 200,000 people have lost their lives and more than 11 million others – nearly half the population – have been forced from their homes during the four years of conflict in Syria.