Islamic State militants pushed on Monday into the eastern edge of the Syrian Kurdish town of Kobani on the Turkish border, after sustained shelling that drove back the Kurdish fighters and Syrian insurgents fighting alongside them, killing 16, Kurdish fighters and activists said.

The Kurdish militants have been hanging on as Islamic State militants have advanced with heavy weapons in a three-week assault. Kurdish women have joined the battle, and one, Kurdish and Syrian activists say, blew herself up with a grenade over the weekend rather than be captured.

Shells have sailed across the Turkish border several times in recent days, and on Monday a black Islamic State flag appeared to be flying from one of the taller buildings in the town of Kobani or Ain al-Arab in Arabic, the main settlement in a group of Kurdish farming villages that has been under assault since mid-September. […]