A spokesman for the Syrian Democratic Forces (SDF) told the AP news agency “the most experienced” jihadists are defending their last stronghold.
Two years ago IS controlled large areas of Syria and Iraq.
But they are now holed up in a tiny pocket in Syria’s eastern province of Deir al-Zour, near the Iraqi border.
On Saturday, after a pause of more than a week to allow some 20,000 civilians to leave the area, SDF spokesman Mustafa Bali said the group was launching the “final battle to crush IS”.
Overnight he told the Associated Press (AP): “The battle is very fierce. Those remaining inside are the most experienced who are defending their last stronghold. According to this you can imagine the ferocity and size of the fighting.”
The SDF, backed by air strikes carried out of the US-led coalition, has driven out IS from towns and villages in north-eastern Syria in recent months.
At its peak in 2014, IS established a “caliphate” stretching across Syria and Iraq that was similar in size to the UK and ruled over more than 7.7 million people.
In December, US President Donald Trump said IS militants were “mostly gone” and announced the US would withdraw all of its 2,000 troops from Syria.
On Wednesday he said: “It should be announced, probably some time next week, that we will have 100% of the caliphate.”
IS’s last stand?
Analysis by BBC Arab Affairs editor Sebastian Usher
Over the past few months, the US-backed SDF has patiently driven IS out of every town and village in the northeast of Syria. The jihadists have been reduced to just a few square kilometres/miles of territory.
In recent days, President Trump has said the total defeat of IS could be declared next week. This suits his agenda of withdrawing all US troops from Syria.
But it’s not the full picture – IS still holds another sliver of territory in Syria further west – while its sleeper cells remain active.
It’s the same story in Iraq. Its ability to continue a guerrilla insurgency persists.
The fate of its hostages, such as the British journalist, John Cantlie, remains unclear – as does that of its leader Abu Bakr al Baghdadi.
How many militants are left?
IS has suffered substantial losses, but the UN says it still reportedly controls between 14,000 and 18,000 militants in Iraq and Syria, including up to 3,000 foreigners.
Meanwhile, there are significant numbers of IS-affiliated militants in Afghanistan, Egypt, Libya, South-East Asia and West Africa, and to a lesser extent in Somalia, Yemen, Sinai and the Sahel.
Individuals inspired by the group’s ideology also continue to carry out attacks elsewhere.