US-backed forces have penetrated the heavily fortified heart of jihadist bastion Raqqa for the first time, in a key milestone in the war against the so-called Islamic State group in Syria.

Air strikes by the US-led coalition battling IS punched two holes in the mediaeval wall surrounding the Old City of Raqqa, allowing fighters of the Syrian Democratic Forces to breach the jihadists' defences, Washington and the SDF said on Tuesday.

The landmark advance in IS's notorious Syria bastion -- the culmination of a seven-month campaign -- comes as the jihadists face an expected defeat within days in Iraq's second city Mosul, the other pivot of the cross-border "caliphate" they declared in 2014.

Coalition officials said a few hundred diehard jihadists were making a desperate last stand in just one square kilometre (less than half a square mile) of Mosul's Old City.

The SDF -- an alliance of Kurdish and Arab forces that has spearheaded the coalition's fightback against IS in Syria -- said its fighters had thrust into the Old City.

It said the two breaches opened by coalition warplanes in the 2.5 kilometre (one and a half mile) wall around the Old City had enabled its fighters to evade the extensive defences the jihadists have put up over the past three years.

"Daesh (IS) have used this archaeological wall to launch attacks, and planted bombs and mines in its gates to hinder the advance of SDF forces," it said on its official Twitter account.

"The precise air strike allowed the opening of two small 25-metre (80-foot) gaps in the wall, allowing the entry of SDF forces avoiding Daesh explosives."

Raqqa became infamous as the scene of some of the group's worst atrocities, including public beheadings, and is thought to have been a hub for planning attacks overseas.

The US envoy to the coalition, Brett McGurk, said on Twitter that breaching the wall of the Old City marked a "key milestone in campaign to liberate the city."

- 'Protected SDF, civilian lives' -

US Central Command, which oversees military operations across the Middle East, said the coalition air strike had not only spared lives among the advancing SDF fighters but also reduced civilian casualties and damage to Raqqa's architectural heritage.

"Conducting targeted strikes on two small portions of the wall allowed coalition and partner forces to breach the Old City at locations of their choosing," the statement read.

This prevented IS from using booby-traps, landmines and suicide car bombs, while it also "protected SDF and civilian lives, and preserved the integrity of the greatest portion of the wall," it said.

The United Nations has raised concerns for tens of thousands of civilians trapped in Raqa, where it says the jihadists are using many as human shields.

The so-called Rafiqah Wall that surrounds the city's historic heart originally dates back to the late 8th Century, when as capital of the Abbasid caliphate, Raqqa was briefly the centre of the Islamic world.

The Syrian Observatory for Human Rights, a Britain-based monitoring group with a wide network of sources on the ground, said the SDF advance had been supported by US special forces.

"This is the most important progress for the SDF since the start of the assault on June 6," Observatory chief Rami Abdel Rahman told AFP.

The US-backed fighters already inflicted a major blow to the jihadists in Raqqa on Sunday, crossing the south back of the Euphrates River that flows through the city to establish a bridgehead on the north bank.

The coalition estimates that some 2,500 IS jihadists are defending Raqa.

That is far more than the 200 or so diehard IS fighters, most of them foreign, that Iraqi commanders believe are holed up in the Old City of Mosul.

- Mosul victory 'in 2 days' -

Iraqi forces were moving in on the last IS-controlled neighbourhoods of the Old City from all sides on Tuesday, commanders said, adding that they expected to announce victory in as few as two days.

"From the early morning, we were able to gain an important foothold in these neighbourhoods," Staff Brigadier General Haidar al-Obeidi, a commander in the elite Counter-Terrorism Service, told AFP.

"In the next two days, we will announce the complete liberation of the Old City, and therefore... the city of Mosul."

Iraqi forces have been closing in on Mosul's Old City for months, but its maze of narrow alleyways combined with a large civilian population has made for an extremely difficult fight.

Iraqi forces are facing a rising number of suicide attacks, including some by female bombers, in the final stages of the more than eight-month-long campaign, commanders said.

But coalition officials said the jihadists were now on their last legs in their two most emblematic strongholds.

"#ISIS terrorists down to less than one square kilometre in #Mosul and totally surrounded in #Raqqa," tweeted US envoy McGurk.