Iraqi forces cleared areas around Fallujah Tuesday after launching an assault to retake the city, tightening their siege on Islamic State group fighters but also raising fears for civilians trapped inside.

With the jihadists surrounded and outnumbered, the recapture of their iconic bastion looked ultimately inevitable, especially after IS suffered a string of losses in recent months.

But illustrating that even a diminished IS is still dangerous, the group has struck back with a wave of bomb attacks, including a series of blasts that left more than 160 dead in Syrian regime coastal strongholds on Monday.

Iraqi Prime Minister Haider al-Abadi declared the start of the operation to retake Fallujah on Monday and less than a day into the battle, Iraqi forces had secured the nearby town of Garma.

That cut off IS fighters in Fallujah from one of their last support areas and paved the way for more advances towards the city, which lies only 50 kilometres (30 miles) west of Baghdad.

"Federal forces advanced towards the east of Fallujah early today from three directions," police Lieutenant General Raed Shakir Jawdat told AFP.

The Hashed al-Shaabi umbrella paramilitary organisation, dominated by Tehran-backed Shiite militias that are heavily involved in the operation, said ground was also gained south of Fallujah.

With forces converging on the city, concerns mounted that the tens of thousands of civilians believed to still be inside had nowhere to go.

- 50,000 civilians trapped -

The Norwegian Refugee Council estimated the number at 50,000 and urged efforts to get them out.

"Families who have been suffering food and medical shortages over the last months now risk being caught in the crossfire and it is absolutely vital that they are granted safe routes out of there so that we can assist them," NRC country director Nasr Muflahi said in a statement.

He told AFP that only 80 families appeared to have been able to flee the city in the hours before the fighting began, and none since.

"We were expecting more to come out overnight, this hasn't happened," Muflahi said, adding that plans by local authorities to open humanitarian corridors had not yet materialised.

Officials from Anbar, the vast western province in which Fallujah is located, reported that small numbers of civilians had managed to sneak out.

A Fallujah resident reached by telephone told AFP there was heavy shelling on the northern edge of the city on Tuesday.

"Daesh (IS) is still imposing a curfew, preventing people from coming out on the street. Some of them are allowed to stand at their gates," said the man, who gave his name as Abu Mohammed al-Dulaimi.

"The number of Daesh members is decreasing and we have started seeing them walk in the street in groups of two or three. We don't know where the others are," he said.

It was unclear what kind of defence IS was prepared to put up in Fallujah, a city that looms large in modern jihadist mythology since 2004 battles that saw US forces suffer some of their worst losses since the Vietnam War.

- 'Extensive air power' -

As the assault began on one of the only two major Iraqi cities IS still holds -- the other being Mosul -- the jihadist group claimed an unprecedented string of bombings in coastal Syrian towns home to President Bashar al-Assad's Alawite minority.

The wave of bombings in Jableh and Tartus on Monday left at least 161 people dead, according to the Syrian Observatory for Human Rights monitoring group.

Iraqi and US-led coalition aircraft have been pounding Fallujah and its surroundings in recent days to support the operation.

The coalition of Western and Arab nations launched air strikes against IS in Syria and Iraq in mid-2014, after the group seized control of large parts of both countries and declared an Islamic "caliphate".

"This operation will again be led by the Iraqi counter-terrorism service (CTS), which made extensive use of air power in the battle of Ramadi, and levelled a great deal of the city," said David Witty, a retired US army special forces colonel.

Ramadi, the capital of Anbar, was lost to IS a year ago and brought back under government control earlier this year.

"This model should not be used in upcoming battles -- they don't want to say they had to destroy the city to save it, or made a wasteland and called it peace," said Witty, a former adviser to the CTS.