Clashes between Syrian Kurds and Isis (now known as the Islamic State) militants have killed over 400 people in the three week battle for the city, according to activists.
The Syrian Observatory for Human Rights said that fighters from the Kurdish side and IS had been killed in the clashes.
The monitoring group said that it had documented 412 deaths from sources on the ground but that the real figure was likely to be double the official toll.
Elsewhere, Turkish President Recep Tayyip Erdogan said that a ground operation was now essential to defeating the radical Islamist group as the city was "about to fall" to the jihadists.
"The terror will not be over... unless we cooperate for a ground operation," he said in a televised speech in the eastern Turkish city of Gaziantep.
"Months have passed but no results have been achieved. Kobani is about to fall [to IS]."
IS has raised two flags to the east of the city, taken control of three districts and is now in control of Mistenur, the strategic hill overlooking the town.
Hundreds of Kurds from the YPG (Syrian-Kurdish militia) have crossed the Syrian-Turkish border to fight the terror group and protect the city, according to YPG spokesman Redur Xelil.
Since the IS offensive on the areas surrounding the city began, approximately 150,000 civilians - mainly Syrian Kurds - have fled across the border into Turkey.