15 October 2014Last updated at 17:09 ET
Idriss Nassan told the BBC IS had lost control of more than 20% of the town in recent days.
US defence officials say hundreds of militants have been killed around Kobane as US-led air strikes intensify.
The news came as US President Barack Obama and European leaders agreed on the need to do more to stop the IS advance in Iraq and Syria.
In a video conference, Mr Obama and the leaders of the UK, France, Germany and Italy agreed to step up support for an "inclusive political approach" in Iraq and training for local forces in Iraq and Syria, a statement by UK Prime Minister David Cameron's office said.
'Cleaning operations' Mr Nassan said Kurdish YPG forces in Kobane were making progress against IS.
"Maybe in the few past days [Islamic State] was controlling about 40% of the city of Kobane, but now... less than 20% of the city is under control of [IS]...," he said.
"Today YPG started cleaning operations in the east and south-east of Kobane."
US defence department spokesman John Kirby said "several hundred" militants had been killed in and around the besieged town, though "it could very well still fall" to IS.
"ISIL has made no secret of the fact that they want that town... and so they have continued to flow fighters to Kobane," he added.
John Allen, US special envoy in the fight against IS, said the strikes were designed to relieve the defenders.
"There was a need for additional fire support to go in to try to relieve the defenders and to buy some white space, ultimately, for the reorganisation on the ground," he said.
US-led forces carried out 18 air strikes on IS targets near the town on Tuesday and Wednesday, US Central Command said in a statement.
Combat positions were destroyed and 16 buildings hit in the strikes. Kurdish fighters have been under siege in Kobane, near the Turkish border, for almost a month.
The coalition has stepped up strikes in the region in recent days, in an effort to prevent IS from capturing the strategically important town.
The BBC's Kasra Naji, on the border near Kobane, says there is an air of optimism among the Kurdish militia, and a belief that they could drive IS out of the town in a few days.
Our correspondent says coalition aircraft now appeared to be targeting a single location, suggesting that this is probably the last neighbourhood in the town held by IS after its strength was degraded by heavy strikes on Tuesday.
The battle for Kobane is regarded as a major test of whether the coalition's air campaign can push back IS in Syria.
More than 160,000 people have fled the predominantly Kurdish town in the face of the IS advance.
'Inherent Resolve' Five more strikes were carried out against IS militants in Iraq - four near Baiji and one near Haditha Dam, US Central Command said.
Meanwhile the jihadists are said to be advancing on the Iraqi town of Amariya al-Falluja, one of the last still controlled by government forces in Anbar province and only 40km (25 miles) from the capital Baghdad.
As the fighting and air strikes continued, the US military announced that it had named the operation against IS "Inherent Resolve".
Mr Obama told a meeting of senior military commanders from more than 20 Western and Arab countries at Andrews Air Force Base near Washington on Tuesday that air strikes would continue in both Kobane and Anbar province.
Mr Obama warned that they were facing a "long-term campaign".
Islamic State 'retreating' in key Syria town of Kobane
Islamic State militants are retreating in parts of the strategic Syrian town of Kobane, a Kurdish official has said.
US defence officials say hundreds of militants have been killed around Kobane as US-led air strikes intensify.
The news came as US President Barack Obama and European leaders agreed on the need to do more to stop the IS advance in Iraq and Syria.
In a video conference, Mr Obama and the leaders of the UK, France, Germany and Italy agreed to step up support for an "inclusive political approach" in Iraq and training for local forces in Iraq and Syria, a statement by UK Prime Minister David Cameron's office said.
'Cleaning operations' Mr Nassan said Kurdish YPG forces in Kobane were making progress against IS.
"Maybe in the few past days [Islamic State] was controlling about 40% of the city of Kobane, but now... less than 20% of the city is under control of [IS]...," he said.
"Today YPG started cleaning operations in the east and south-east of Kobane."
US defence department spokesman John Kirby said "several hundred" militants had been killed in and around the besieged town, though "it could very well still fall" to IS.
"ISIL has made no secret of the fact that they want that town... and so they have continued to flow fighters to Kobane," he added.
John Allen, US special envoy in the fight against IS, said the strikes were designed to relieve the defenders.
"There was a need for additional fire support to go in to try to relieve the defenders and to buy some white space, ultimately, for the reorganisation on the ground," he said.
US-led forces carried out 18 air strikes on IS targets near the town on Tuesday and Wednesday, US Central Command said in a statement.
Combat positions were destroyed and 16 buildings hit in the strikes. Kurdish fighters have been under siege in Kobane, near the Turkish border, for almost a month.
The coalition has stepped up strikes in the region in recent days, in an effort to prevent IS from capturing the strategically important town.
The BBC's Kasra Naji, on the border near Kobane, says there is an air of optimism among the Kurdish militia, and a belief that they could drive IS out of the town in a few days.
Our correspondent says coalition aircraft now appeared to be targeting a single location, suggesting that this is probably the last neighbourhood in the town held by IS after its strength was degraded by heavy strikes on Tuesday.
The battle for Kobane is regarded as a major test of whether the coalition's air campaign can push back IS in Syria.
More than 160,000 people have fled the predominantly Kurdish town in the face of the IS advance.
'Inherent Resolve' Five more strikes were carried out against IS militants in Iraq - four near Baiji and one near Haditha Dam, US Central Command said.
Meanwhile the jihadists are said to be advancing on the Iraqi town of Amariya al-Falluja, one of the last still controlled by government forces in Anbar province and only 40km (25 miles) from the capital Baghdad.
As the fighting and air strikes continued, the US military announced that it had named the operation against IS "Inherent Resolve".
Mr Obama told a meeting of senior military commanders from more than 20 Western and Arab countries at Andrews Air Force Base near Washington on Tuesday that air strikes would continue in both Kobane and Anbar province.
Mr Obama warned that they were facing a "long-term campaign".
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