PARIS (Reuters) - French prosecutors said on Saturday that three coordinated teams of gunmen and suicide bombers carried out a wave of attacks across Paris that killed 129 people in what President Francois Hollande called an "act of war" by Islamic State.

Hollande declared a state of emergency, ordering police and troops into the streets, and set three days of official mourning as a stunned nation sought to comprehend the simultaneous assault on restaurants, a concert hall and the national soccer stadium on a busy Friday evening.

As a cross-border investigation gathered pace, prosecutors said the slaughter - claimed by Islamic State as revenge for French military action in Syria and Iraq - appeared to involve a multinational team with links to the Middle East, Belgium and possibly Germany as well as home-grown French roots.

Ominously, Greek officials said one and perhaps two of the assailants had passed through Greece from Turkey alongside Syrian refugees fleeing violence in their homeland.

In the worst carnage, three gunmen systematically killed at least 89 people at a rock concert by an American band at the Bataclan theater before detonating explosive belts as anti-terrorist commandos launched an assault, officials said.

Some 40 more people were killed in five other attacks in the Paris region, including a double suicide bombing outside the Stade de France stadium, where Hollande and the German foreign minister were watching a soccer international. By Saturday night, 99 people were still in critical condition.

The bloodshed came as France, a founder member of the U.S.-led coalition waging air strikes against Islamic State, was already on high alert for terrorist attacks, raising questions about how such a complex conspiracy could go undetected.

It was the worst such attack in Europe since the Madrid train bombings of 2004, in which Islamists killed 191 people.