A man stabbed two officers and took their guns before shooting them and a 22-year-old man sitting in a vehicle parked nearby.
He took a woman hostage in a school before being himself shot dead by police.
A senior official at the federal prosecutor’s office said there were “indications it could be a terror attack”.
In a message on Twitter shortly after the outrage, Mrs May said: “My thoughts are with the victims of today’s cowardly attack in Belgium and their grieving families.
“The UK stands resolute with our Belgian allies against terror.”
Belgian prime minister Charles Michel has so far described the attack as “a serious incident”. The country’s federal crisis centre said there was “absolutely no confirmation yet that the incident is terror-related”.
Video posted on Twitter by a person claiming to be a witness showed people running in the area.
About six gunshots could be heard.
Metropolitan Police Commissioner Cressida Dick also condemned the attack, saying: “I am immensely saddened to hear of the terrible attack on police officers in Liege, Belgium today.”
Despite the potential terrorism link, Belgium’s crisis centre said it saw no reason to raise the country’s terror threat alert for now.
When asked about the report that the attack was terror-related, Liege city hall Michel Firket said: “I know nothing formal about that. The police is doing its investigation. There are no formal conclusions.”
A spokeswoman for the city mayor’s office, Laurence Comminette, told reporters the children at the school were all safe.
Belgian police and military have been on alert since suicide bombers killed 32 people at the Brussels airport and subway system in 2016.