A commander of the Kurdish militia defending the northern Syrian town of Kobane says Islamic State (IS) fighters have been driven from all but two areas.
Baharin Kandal told the BBC that IS fighters had retreated from all areas, except for two pockets of resistance in the east.
US-led air strikes have helped push back the militants, with another 14 conducted over the past 24 hours.
Meanwhile, new UN human rights commissioner Zeid Ra'ad al Hussein has described IS as a "potentially genocidal" movement.
Activists say more than 600 people have been killed since the jihadist group launched its assault on Kobane a month ago.
Major test for US-led air campaign
Speaking by phone, Kurdish commander Baharin Kandal told the BBC's Kasra Naji that she hoped the city would be "liberated soon".
Ms Kandal said her militia group had been receiving arms, supplies and fighters but she refused to say how.
The battle for Kobane, which is also known as Ayn al-Arab, is regarded as a major test of whether the US-led coalition's air campaign can push back IS.
US Central Command said that bomber and fighter aircraft had conducted 14 air strikes on Wednesday and Thursday, all of them targeting IS around Kobane.
The strikes "successfully struck 19 IS buildings, two IS command posts, three IS fighting positions, three IS sniper positions, one IS staging location and one IS heavy machine gun", a statement said.
It said the air strikes had "continued to slow IS advances, but that the security situation on the ground in Kobane remains tenuous".
The ABC reports that Australian F-18 Super Hornet jets have killed an unspecified number of people in Northern Iraq, said to be Islamic State fighters.
The RAAF fighter-bombers have increased their sorties over Iraq in the past week to allow the American and other coalition air forces to concentrate their bombing activity in Syria in the fight for the city of Kobane.
Meanwhile, the Australian Department of Foreign Affairs and Trade is urging any Australians who are still in Iraq to leave immediately. It said people should get out of the country while Baghdad International Airport is open and commercial flights are still operating.