French police have identified three teams of gunmen wearing suicide vests who killed at least 129 people in Paris's worst ever attacks that were claimed by the Islamic State group and prompted a global outpouring of solidarity with the victims.

A 29-year-old Frenchman was the first to be identified among the seven attackers, all of whom died in the assault, prosecutors said, while at least one man under investigation over the atrocities had registered as a Syrian refugee in Greece.

The discovery of a Syrian passport near the body of one attacker has raised suspicions some of them might have entered Europe as part of an influx of people fleeing Syria's civil war.

"We confirm that the (Syrian) passport holder came through the Greek island of Leros on October 3 where he was registered under EU rules," said the Greek minister for citizen protection, Nikos Toskas.

Earlier in the day, the Islamic State militant group claimed responsibility for the gun and suicide attacks that left a trail of destruction at a sold-out concert hall, at restaurants and bars, and outside France's national stadium.

A total of 129 people were killed and 352 wounded, of whom 99 were said to be in critical condition. The toll does not include the attackers.

President Francois Hollande called the coordinated assault on Friday night an "act of war" as the capital's normally bustling streets fell eerily quiet, 10 months after attacks on magazine Charlie Hebdo shocked the nation.

READ: 'It is horror': French President Hollande's remarks after Paris attacks

The attacks sent shockwaves around the world, with London's Tower Bridge, Berlin's Brandenburg Gate and the World Trade Center in New York among the many landmarks lit up in the red, white and blue of the French tricolour in a show of solidarity.

Mourners also broke out in stirring renditions of the French anthem "La Marseillaise", including at a rally in Dublin and at New York's Metropolitan Opera.

PHOTOS: #PrayForParis : World monuments light up blue, white and red

Gunman identified

US President Barack Obama described the onslaught as "an attack on all of humanity" and an emotional Pope Francis said he was "shaken" by the "inhuman" attacks.

British Prime Minister David Cameron said the attacks "suggest a new degree of planning and coordination and a greater ambition for mass casualty attacks".

The remains of the 29-year-old French gunman were found near the Bataclan concert hall in eastern Paris, the site of the bloodiest attack.

Police have since taken into custody the father and brother of the gunman and were searching their homes, a source close to the probe told AFP.

A total of 89 people were killed at the Bataclan by the armed men who burst in shouting "Allahu akbar" (God is greatest) before gunning down concert-goers and executing hostages.

The militants were heard raging at the French president and his decision in September to begin air strikes on Islamic State targets in Syria.

In a statement posted online Saturday, IS claimed responsibility for the attacks and referred to French air strikes on IS in Syria.

The group, which has sown mayhem in large swathes of Syria and Iraq, threatened further attacks in France "as long as it continues its Crusader campaign."

The band on the Bataclan's stage during the attack, US rock group Eagles of Death Metal, survived but have cut short their European tour to return to the United States, promoters said.

As police stormed the venue, two of the gunmen blew themselves up, while the third was shot by police.

Three suicide bombers also detonated their explosives outside the Stade de France stadium where France were playing Germany in a football friendly attended by Hollande, who was evacuated.

The seventh attacker blew himself up on a bustling avenue near the concert hall, injuring one other person.

The explosions marked the first-ever suicide bombings on French soil.

Analysts at Eurasia Group said the attacks "confirm a structural shift in the modus operandi of the Islamic State, and represent a prelude to additional attacks in the West."

European investigation

The investigation spread beyond France on Saturday as Belgian police arrested several suspects in Brussels, including one who was in Paris at the time of the carnage.

The arrests -- local media said three people were detained -- were in connection with a vehicle found near the Bataclan concert hall, they said.

In Germany, the authorities said they were looking into a possible link between the attacks and the arrest in Bavaria last week of a man with a car-load of weapons and explosives.

The Paris attacks were "prepared, organised and planned overseas, with help from inside (France)," Hollande said.

In Greece -- the main entry point into Europe for hundreds of thousands of migrants fleeing conflict and misery -- police were investigating a possible Syrian connection to the Paris attacks, though they did not rule out that the Syrian passport may have changed hands before the assault.

READ: Two men linked to Paris attacks registered as migrants in Greece: police

Within conflict-torn Syria, residents and activists from some of the country's most war-ravaged areas joined the global outcry over the carnage in Paris.

"We extend our hands to all the people that love peace and freedom, most of all the French people," residents of the besieged town of Douma near Damascus wrote in an open letter.

As well as the stadium and the concert hall, several restaurants were also targeted in Friday's violence, including a popular Cambodian eatery in the trendy Canal St. Martin area, where at least 12 people died.

Another 19 people were killed at a busy restaurant on nearby Rue de Charonne.