Kurdish Peshmerga fighters have fought their way to Iraq’s Sinjar Mountains where hundreds of people have been trapped for months by fighters of the Islamic State of Iraq and the Levant (ISIL) group, a Kurdish official has said.

“Peshmerga forces have reached Mount Sinjar, the siege on the mountain has been lifted,” Masrour Barzani, head of the Iraqi Kurdish region’s national security council, told reporters from an operations centre near the border with Syria on Thursday.

The assault, backed by US-led air strikes, ended the months-long ordeal of hundreds of people from Iraq’s Yazidi minority, who had been besieged on the mountain since ISIL stormed Sinjar and other Kurdish-controlled parts of northern Iraq in August, he said.

“All those Yazidis that were trapped on the mountain are now free,” Barzani said, but added that the Peshmerga had not yet begun to evacuate them.

He said 100 ISIL fighters had been killed – a claim that could not be independently verified.

Kurdish Peshmerga soldiers began their offensive on Wednesday to break the Sunni armed group’s siege of the mountain and the town of Sinjar.

Lieutenant General James Terry, head of the US-led campaign against ISIL, said more than 50 air strikes in recent days “have resulted in allowing those [Kurdish] forces to manoeuvre and regain approximately 100 square kilometres of ground” near Sinjar.

Meanwhile, the Pentagon said on Thursday that US strikes had killed several top ISIL leaders.

“I can confirm that since mid-November, targeted coalition air strikes successfully killed multiple senior and mid-level leaders,” Rear Admiral John Kirby. the Pentagon spokesman, said.

US officials said among those killed was Abu Muslim al-Turkmani, who was Baghdadi’s deputy in charge of Iraq and would be the most senior ISIL leader to fall this year.

The capture of Sinjar by ISIL fighters and the plight of the mostly Yazidi population there was cited by President Barack Obama as one of the reasons for the US military intervention in Iraq.

Al Jazeera’s Sue Turton, who is in Iraq, reports about the recent gains by the Kurdish fighters and their significance

What do we know for certain about what’s happening on the ground?

There was a military build-up of Peshmerga forces. We drove through right from the Sinjar Mountains across the length of northern Iraq two nights ago, and we saw the build-up of military hardware, with various troops along that route. However, it wasn’t an enormous amount of military build-up and this is why we have to be slightly cautious because Masoud Barzani, president of Iraq’s Kurdistan region, and the Peshmerga are saying in Erbil that 8,000 Peshmerga are pushed a distance of 700sq/km from Zumar, which is south of the Mosul Dam area all the way into the Syrian border. They’re taking towns and villages that ISIL has controlled for a long time along the way. They’re saying that they’ve taken the mountain range next to Tal Afar, which is where the main ISIL military base is. They say that they can now shoot down on that military base. Indeed, they’ve even stretched along the three mountain ranges all the way to the main Sinjar Mountains, which is where we were just a few days ago. This area remains besieged now since the summer, and the ISIL fighters have really been pushing on for many weeks. The Peshmerga have been telling us that they’re running out of ammunition and that they’re really on the backfoot. So to say that they have managed to take this whole ground is an extraordinary achievement if indeed it is the case. But I think we should also question as to where ISIL fighters have gone to. They say they’ve killed over a 100 ISIL fighters but that begs the question if ISIL has really just disappeared into the communities and has sort of pulled back into Mosul city and is really waiting or laying siege until they want to reappear and strike back. Why are the Sinjar Mountains important?