It was not immediately clear what motivated the attack in the busy Place Saint-Lambert square, the central entry point to downtown shopping streets in the city in eastern Belgium. The attack prompted hundreds of shoppers to stampede down old city streets, fleeing explosions and bullets.
Interior Ministry official Peter Mertens said the attack did not involve terrorism but did not explain why he thought that.
Belgian officials identified the attacker as Nordine Amrani, 33, a Liege resident who they said had done jail time for offenses involving guns, drugs and sexual abuse. He was among the dead, but Liege Prosecutor Danielle Reynders told reporters it was unclear if he committed suicide or died by accident. He did not die at the hands of police, she said.
The other dead were two teenage boy students aged 15 and 17 and a 75-year-old woman, while an 18-month-old toddler died Tuesday evening in the hospital, Liege police said.
Reynders said Amrani had been summoned for police questioning on Tuesday but the reason for that was not clear. He still had a number of grenades with him when he died, she said.
Officials said Amrani left his home in Liege with a backpack, armed with hand grenades, a revolve and an FAL assault rifle. He walked alone to the central square, then got onto a platform that gave him an ideal view of the square below, which was bedecked with a huge Christmas tree and crowded with shoppers.
From there, Amrani lobbed three hand grenades toward a nearby bus shelter, which serves 1,800 buses a day, then opened fire upon the crowd. The explosions sent shards of glass from the bus shelter across a wide area.
"I heard a loud boom," said witness Dimitri Degryse. "I thought it was something on my car that was broken or something. Then a few seconds after a second boom, and I saw all the glass breaking, I saw people running, screaming."
As soon as the shooting began, hundreds fled the square as well as a nearby Christmas market. Video from the scene showed people, including a large group of children, rampaging through the city center to seek cover, some still carrying shopping bags.
As police hunted for possible accomplices, residents were ordered to stay in their homes or seek shelter in shops or public buildings. As sirens howled and a police chopper roared overhead, a medical post was set up in the nearby courtyard of the Prince Bishops courthouse. Dozens of emergency vehicles took victims away for treatment.
Police closed off the area but found no accomplices and calm returned a few hours after.
The Place Saint-Lambert and the nearby Place du Marche host Liege's annual Christmas market, which consists of 200 tiny shops and attracts some 1.5 million visitors a year. By dusk, with the Christmas lights gleaming again, King Albert II and Queen Paola came to pay their respects, as did Prime Minister Elio Di Rupo.
Herman Van Rompuy, a former Belgian prime minister who is now president of the European Council, said he was badly shaken by the attack.
"There is no explanation whatsoever," Van Rompuy said. "It leaves me perplexed and shocked."
While officials excluded terrorism as a motive for Amrani's attacks, Europe has experienced several recent terror attacks.
In Italy on Tuesday, a man opened fire in an outdoor market in Florence, killing two vendors from Senegal and wounding three other immigrants before killing himself, authorities said. Investigators identified the attacker as 50-year-old Gianluca Casseri, and RAI state TV said he was known to police for having participated in racist marches by an extreme right-wing group.
In Norway last July, far-right extremist Anders Behring Breivik went on a bomb and shooting spree that killed 77 people around Oslo, apparently motivated by a hatred of Muslim immigrants and a deep grudge against the governing Labor Party. A psychiatric evaluation found him criminally insane, which if upheld by the courts means he would end up in compulsory psychiatric care instead of prison.
Belgium, also has not been immune to this sort of violence.
In the early 1980s, a group of heavily armed gunmen dubbed the "mad killers of Brabant" terrorized supermarkets and other stores in the Brabant region around Brussels. The gunmen fired apparently at random at bystanders during a series of robberies between 1982 and 1985, killing 28 people in all.
The scale of the bloodshed, the military weapons used, and the fact that the robberies often involved relatively small amounts of money sparked suspicions that right-wing terrorists may have been behind the attacks. But there were no claims of responsibility and the identity of the attackers remains unknown to this day.