Belgian police found an Islamic State flag next to the body of an Algerian killed during a raid in Brussels, investigators said Wednesday as they raced to track down two suspected extremists who escaped.

The assailant has been named as Mohamed Belkaid, 35, an Algerian national living illegally in Belgium, who was killed by a police sniper while trying to fire at police from a window during a chaotic gunbattle on Tuesday.

Two suspects were still at large after the bloodshed, which erupted as Belgian and French police searched a property in connection with the November Paris massacre claimed by IS in which 130 people died.

Belgian Prime Minister Charles Michel said authorities had decided to maintain the country's terror alert at the second-highest level of three, "which means a threat is possible and likely".

Brussels was locked down and the alert level raised to the highest of four shortly after the Paris attacks, but it was lowered back to three a few days later, although troops remain outside many key sites.

 Rifle and flag

 Prosecutors said that at least two armed suspects fired on police as the door was opened during a search of the property in the quiet Forest district in southern Brussels, wounding three officers including a French policewoman.

After hours of gunbattles in which a fourth officer was hurt, a suspect was "neutralised by a sniper of the special forces when he tried to open fire from the window of the flat", spokesman for the prosecutors Thierry Werts said.

"Next to his body was a Kalashnikov, a book on Salafism (an extreme form of Islam) and an Islamic State flag," Werts told a press conference. Eleven magazines of ammunition for Kalashnikov assault rifles were also found.

Belkaid was unknown to Belgian authorities except for a case of minor theft in 2014, they said.

Werts said that "two persons who were probably in the flat and whose identity is not known fled the scene and are being tracked down".

A second Kalashnikov and black clothes were found abandoned at a house nearby but searches throughout the southern district of Brussels for the two men yielded "no results", he said.

Two suspects arrested in connection with the case, including one found in hospital with a broken leg, were later released without charge, prosecutors added.

Belgian media reported that the two missing suspects were brothers with links to terrorism but there was no immediate confirmation.

 Brussels extremist history

 Children were left trapped in nearby schools by the shootout, and Michel thanked residents for their "composure" as bursts of gunfire erupted in the streets and dozens of heavily-armed police with balaclavas and sub-machineguns patrolled.

By early Wednesday calm had largely returned to the area and most locals had been allowed to return home. 

Counsellors were sent to the reopened schools to help teachers, parents and the small children cope with the aftermath, RTBF radio reported.

Access to the scene of the shootout was also reopened with the windows in the building blown out and taped up with plastic.

The mayor of Forest, Marc-Jean Ghyssels, said that life was back to normal.

"There wasn't a direct threat to the public, it's a search that turned bad," he said.

Belgium has been at the centre of the investigation into the Paris attacks almost from day one, with President Francois Hollande saying they were planned there.

Key Paris suspect Salah Abdeslam fled to Brussels after the attacks and is believed to have holed up in a flat for at least three weeks. He remains on the run while his brother Brahim blew himself up in the massacre.

The ringleader of the attacks, Islamic State member Abdelhamid Abaaoud, was also from Brussels. He was killed in a raid in Paris in November.

Both had links to the largely immigrant Brussels district of Molenbeek which was targeted by authorities after the attacks.

Meanwhile in Paris four suspected jihadists were arrested Tuesday, one of whom was thought to be planning "violent acts", French Interior Minister Bernard Cazeneuve said.

The four had been under surveillance by French intelligence on suspicion of a "possible plan to attack", police sources said. 

Police raids turned up no weapons, but computer hardware and data have been seized for analysis, they said.