The militants entered an eastern district of the city and raised a flag but were forced to withdraw after less than an hour, Can Memis, a member of a pro-Kurdish party, said by phone from the border village of Behte. Fighting raged over the Mistenur hill east of Kobani, where a female Kurdish fighter blew herself up in a suicide attack against the jihadists late yesterday, according to Kurdish reports.

The Kurds are determined to hold on to Kobani because they see Islamic State as trying to scatter the Kurdish population in order to weaken a future autonomous region

At stake for the Kurds defending the town, also known as Ayn al-Arab, is the fate of the autonomous region they set up in 2013 as the Syrian government lost control of large swaths of territory to rebels during the civil war. Thousands have fled across the border into Turkey since the Islamic State of Iraq and Al-Sham launched its offensive last month with tanks and heavy artillery to take the town defended by lightly armed Kurds.

“The Kurds are determined to hold on to Kobani because they see Islamic State as trying to scatter the Kurdish population in order to weaken a future autonomous region,” said Theodore Karasik, director of research at the Institute for Near East and Gulf Military Analysis in Dubai. Islamic State want to capture Kobani “to cleanse” territory of groups that will resist its rule and to control the border, he said.

More than 45 fighters, including 27 Islamic State militants, died in the clashes yesterday around Kobani, according to the U.K.-based Syrian Observatory for Human Rights, which is monitoring the conflict via local activists. The Observatory says that few civilians remain in the town.

The militants are seeking to expand their self-declared caliphate that stretches across much of northern Iraq and Syria. In a bid to stop their gains, fighter jets from Canada, the U.S. and their allies have struck ISIS positions in both countries. Kurdish leaders have accused the coalition, and Turkey, of not doing enough to save Kobani.

U.S. Central Command said in a statement that the coalition carried out nine strikes against ISIS targets in Syria and Iraq yesterday and the previous day. Warplanes struck areas around Kobani at about 2 a.m. local time, Ismail Kaplan, local head of the pro-Kurdish People’s Democracy Party, said by phone from the border town of Suruc.

As the fighting closed in on Kobani, Turkey ordered residents of some nearby border areas to leave for their own safety. Turkey has pledged to join the U.S.-led campaign against ISIS, without specifying what it will do. The government’s main goal in Syria has been the removal of President Bashar Al-Assad’s regime.

The Syrian Kurds fighting in Kobani have links to the Kurdistan Workers’ Party, or PKK, which has been fighting for autonomy in Turkey for three decades, and is classified as a terrorist group by Turkey and the U.S.

That “may partly explain the Turkish wait-and-see approach to this battle,” Paul Sullivan, a Middle East specialist at Georgetown University in Washington, said in response to e- mailed questions.

Turkish officials told the leader of the Syrian Kurdish fighters, Salih Muslim Mohamed, that they might give tacit approval for arms shipments to reach Kobani if the Kurds refrain from declaring an autonomous region in Syria and join the Free Syrian Army battling against Assad, Milliyet newspaper reported today, without saying where it got the information.

Kurdish politicians in Syria and Turkey have complained of a lack of international support, and say Turkey is seeking to quash the development of Kurdish self-rule in Syria.