Iraqi Kurdish leader Massud Barzani hailed victories over the Islamic State jihadist group during a visit on Sunday to Mount Sinjar, which had been besieged by the militants for months.

Thousands of the autonomous Kurdish region's peshmerga fighters launched a major operation backed by US-led air strikes on Wednesday which broke the second IS siege of Mount Sinjar this year.

The Kurdish offensive threatens the links between the city of Mosul, the main IS stronghold in Iraq, and territory the militant group controls in neighbouring Syria.

"During the past 48 hours, the peshmerga opened two main routes to Mount Sinjar," Barzani said, adding: "We did not expect to achieve all these victories."

In addition to breaking through to the mountain, "a large part of the centre of the town of Sinjar was also liberated," he said, referring to the district's main settlement to the south of the mountain.

The Kurdish regional president said the peshmerga might participate in an operation to retake Mosul itself.

"We will take part if the Iraqi government asks us, and of course we will have our conditions," he said, without specifying what they would be.

IS spearheaded a sweeping offensive that has overrun much of Iraq's Sunni Arab heartland since June, presenting both an opportunity for territorial expansion and an existential threat to the country's Kurdish region.

Multiple Iraqi divisions collapsed in the early days of the advance, clearing the way for the Kurds to take control of a swathe of disputed northern territory that they have long wanted to incorporate into their autonomous region over Baghdad's objections.

But after driving south towards Baghdad, IS then turned its attention to the Kurds, pushing them back towards their regional capital Arbil in a move that helped spark US air strikes against the jihadists.

Backed by the strikes, which are now being carried out by a coalition of countries, Kurdish forces have clawed back significant ground from IS.

The conflict seems set to redraw the internal boundaries of Iraq in favour of broader Kurdish control in the north.

In his remarks on Mount Sinjar, Barzani said: "We will not leave an inch of the land of Kurdistan for (IS), and we will strike (IS) in any place it is located."

Tens of thousands of members of the Yazidi religious minority were trapped on the mountain for days in the searing August heat in the first IS siege, which sparked fears of genocide.

That siege was broken and many of the civilians evacuated, but others stayed behind and were again besieged by the jihadist group in October.

While both Kurdish and federal forces have made gains against IS, the group remains a potent threat, holding extensive territory in Iraq and eastern Syria.

IS militants launched a major assault Saturday on the strategic town of Baiji, south of Mosul, sparking fighting that lasted into the following day.

The province's governor and an army officer said the attack was repulsed, while two other officers said that pro-government forces lost ground.

Iraqi Prime Minister Haider al-Abadi meanwhile travelled to Kuwait on Sunday for talks expected to focus on the security situation among other issues, his office said.

The visit came just days after the UN said Iraq could delay payment of a final $4.6 billion in war reparations for its 1990 invasion of Kuwait due to the "extraordinarily difficult security circumstances".