Three people were killed and an estimated 125 wounded when the man threw hand grenades and opened fire, killing himself afterwards.
Prime Minister Elio Di Rupo, who has only been in office since last week, said there were "no words to describe this tragedy".
"The whole country shares the pain of the families affected. We share the shock of the population," he said as he visited the square on Tuesday where the tragedy unfolded.
David Cameron has passed on Britain's sympathies. A Downing Street spokesman said he "called the Belgian Prime Minister this evening to pass on his sympathy in the wake of the appalling attacks in Liege.
"He said that his thoughts and those of very many people in Britain were with all those involved."
The killer has been identified as Liege resident Nordine Amrani.
He was known to police for previous drugs and firearms offences – he had spent three years in jail but was let out on parole in October 2010.
Officials have ruled out political terrorism as a motive, but are yet to determine why he opened fire.
No note has been found and Amrani has no history of mental illness.