RAQQA - U.S.-backed militias will capture Islamic State's last foothold in the jihadists' former Syrian capital of Raqqa within hours, a militia spokesman said on Tuesday.

A Reuters witness said the fighting appeared to be almost at an end, with only sporadic bursts of gunfire. Militia fighters celebrated in the streets and chanted slogans from their vehicles.

A local field commander said no Islamic State fighters remained even in their two remaining city strongholds.

Fighting on Monday night and Tuesday has focused on Raqqa's National Hospital and the nearby city stadium, two central positions in which it was well entrenched.

The fall of Raqqa city, where Islamic State staged euphoric parades after its string of lightning victories in 2014, is a potent symbol of the jihadist movement's collapsing fortunes. From the city, the group planned attacks abroad.

It is now hemmed in to a tiny bomb-cratered patch of the city around the stadium that is pounded from the air by a U.S.-led coalition and encircled by Syrian Democratic Forces (SDF) fighters.

Islamic State has lost swathes of territory in Syria and Iraq this year, including its most prized possession, Mosul, and in Syria it has been forced back into a strip of the Euphrates valley and surrounding desert.

The SDF, an alliance of Kurdish and Arab militias, took the National Hospital in fierce fighting overnight and early on Tuesday, said spokesman Mostafa Bali in a statement.

"During these clashes, the National Hospital was liberated and cleared from the Daesh mercenaries, and 22 of these foreign mercenaries were killed there," said Bali, using the Arabic acronym for Islamic State.

Another SDF spokesman, Talal Silo, said he believed all fighting around the hospital and the stadium would end in the coming hours.

An SDF field commander who gave his name as Ager Ozalp said three militiamen had been killed on Monday by mines that have become an Islamic State trademark in its urban battles.

Another field commander, who gave his name as Abjal al-Syriani, said SDF fighters had entered the stadium and found burned weapons and documents.

He had heard estimates of about 100 Islamic State fighters remaining in their last besieged pocket, Ozalp said.

The stadium has become the last major position held by Islamic State after four months of battle in Raqqa and the departure of some of its fighters on Sunday, leaving only foreign jihadists to mount a last stand.

The SDF has been supported by a U.S.-led international coalition with air strikes and special forces on the ground since it started the battle for Raqqa city in early June.

The final SDF assault began on Sunday after a group of Syrian jihadists quit the city under a deal with tribal elders, leaving only a hardcore of up to 300 fighters to defend the last positions, including the hospital and stadium.

Raqqa was the first big city Islamic State captured in early 2014, before its rapid series of victories in Iraq and Syria brought millions of people under the rule of its self-declared caliphate, which passed laws and issued passports and money.

It used the city as a planning and operations centre for its warfare in the Middle East and its string of attacks overseas, and for a time imprisoned Western hostages there before killing them in slickly produced films distributed online.

The SDF advance since Sunday also brought it control over a central city roundabout, where Islamic State once displayed the severed heads of its enemies, and which became one of its last lines of defence as the battle progressed.

(Additional reporting by Ellen Francis and Dahlia Nehme in Beirut; Writing by Angus McDowall in Beirut; Editing by Matthew Mpoke Bigg) ((angus.mcdowall@thomsonreuters.com))