A US-backed Kurdish-Arab alliance pushed closer to Raqa in Syria while Iraqi forces seized a key town near Mosul as offensives advanced Monday against the two Islamic State group strongholds.

After announcing the launch of the long-awaited assault on Raqa on Sunday, the Syrian Democratic Forces (SDF) alliance said it had moved south towards the city despite fierce jihadist resistance.

South of Mosul, Iraqi forces retook Hamam al-Alil from IS, a key objective in their three-week advance on the city.

Iraqi forces said they found a mass grave in the area containing around 100 decapitated bodies.

Raqa and Mosul are the last major cities in Syria and Iraq under the jihadists' control.

Their capture would deal a knockout blow to the self-styled "caliphate" IS declared in mid-2014.

The US-led coalition that launched operations against IS two years ago is providing crucial backing to the offensives, with air strikes and special forces advisers on the ground.

SDF spokeswoman Jihan Sheikh Ahmed told AFP that the alliance's forces had advanced on two fronts towards Raqa amid heavy fighting.

SDF fighters had pushed at least 10 kilometres (six miles) south towards the city from the towns of Ain Issa and Suluk, she said.

In both cases the SDF was still some distance from Raqa -- on the Ain Issa front at least 30 kilometres (20 miles) away.

"The offensive is going according to plan," said Ahmed, adding that the SDF had captured at least 10 villages.

- 'Fight will not be easy' -

An SDF commander said IS was fighting back with its favourite tactic of sending suicide bombers in explosives-packed vehicles against advancing forces.

"IS is sending car bombers but coalition planes and our anti-tank weapons are limiting their effectiveness," the commander said, speaking on condition of anonymity.

After taking Abu Ilaj north of Raqa, SDF fighters dug trenches and piled sandbags at the entrance to the village.

"In every area that we advance we are digging trenches with tractors and bulldozers to protect the front line, to prevent the jihadists from getting in and to stop car bombs," one fighter said.

The SDF says some 30,000 of its fighters are taking part in operation "Wrath of the Euphrates" which aims to surround and isolate IS inside Raqa before assaulting the city itself.

Officials have warned that the battle is likely to be long and difficult.

"As in Mosul, the fight will not be easy and there is hard work ahead," US Defence Secretary Ashton Carter said.

"But it is necessary to end the fiction of ISIL's caliphate and disrupt the group's ability to carry out terror attacks against the United States, our allies and our partners," Carter said, using an alternative name for IS.

Driving IS from both cities has been the endgame since the US-led coalition launched air strikes against it in summer 2014, shortly after the jihadists seized large parts of Syria and Iraq.

Some 50 US military advisers are involved in the Raqa operation, particularly to guide air strikes, according to an SDF source.

Near Mosul, federal police, army and elite interior ministry forces established full control over Hamam al-Alil, the last town of note on the way to the city from the south, AFP reporters said.

It lies on the west bank of the Tigris river, about 15 kilometres (nine miles) southeast of the edge of Mosul.

Life quickly resumed in Hamam al-Alil, with some residents reopening shops and others bathing in the town's sulphur springs.

- Mass grave found -

However, police said they found a mass grave Monday at an agricultural collage west of Hamam al-Alil.

The Joint Operations Command said "Iraqi forces found... 100 bodies of citizens with their heads cut off".

Fighting also continued east of Mosul, with Kurdish forces advancing into the town of Bashiqa and the elite Counter Terrorism Service battling IS in the city's suburbs.

"Up to seven neighbourhoods are under the control of counter-terrorism forces, and they are now completely securing them and clearing them of pockets of terrorists present inside the houses," CTS spokesman Sabah al-Noman told AFP.

A peshmerga statement said late Monday its forces were in Bashiqa and had "begun house-to-house clearances".

The Mosul offensive has advanced faster than expected, but the battle for Raqa is more complicated.

Unlike in Iraq where the coalition has a state-controlled ally in federal forces, in Syria its ground partner is comprised of local militias, including some rebel groups that have battled President Bashar al-Assad's regime.

The domination of the SDF by the Kurdish People's Protection Units (YPG) has also raised deep concerns in Turkey, which considers the YPG a "terrorist" group linked to the outlawed Kurdistan Workers' Party (PKK).

Aid groups have voiced concerns for civilians trapped in both Mosul and Raqa, warning they may be used as human shields.

More than 34,000 people have been displaced since the Mosul operation began on October 17, the International Organization for Migration said on Monday.

A US government official put the number at "just over 33,000 people".

More than a million people are believed to be in Mosul.

Raqa had a population of some 240,000 before 2011 but more than 80,000 people have since fled there from other parts of Syria.

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