The Belgian Red Cross has made an appeal for blood donations as hospital workers rush to treat scores of injured people.
Facebook has activated at ‘safety check’ status for people in the Brussels area to tell their loved ones they are safe.
The border between France and Belgium has been shut down following the attacks, with roads, rail and air services closed.
French authorities will bar members of the public without tickets or identification from entering transports hubs.
Security at European institutions in Strasbourg have also been reinforced.
Belgian authorities have also stepped up security at nuclear sites.
A Slovenian diplomat was injured in the Brussels attacks on Tuesday, Slovenian Foreign Minister Karl Erjavec said.
Mr Erjavec told a news conference that the diplomat, who he did not name, was hurt in the metro blast on his way to work.
He said the diplomat was being treated in hospital but his injuries were not life threatening.
David Cameron said security would now be stepped up at ports, airports and train stations.
He said: “We have held a COBRA meeting to make sure we are doing everything we can and we are enhancing security.
“These are difficult times, they are appalling terrorists and we will stand together to do everything we can.
“Although they attack our way of life and who we are, we will never let them win.
“We still have information coming in. If there is information that advises there is a direct threat to Britain we will raise the security threat level.
“We will continue to keep the situation under review and make sure we do everything we can.
“We face a very real terrorist threat right across the different countries in Europe.
“It’s too early to say (about British victims) but we will make announcements when we have hard information.”
US President Barack Obama, speaking from Cuba, said: “We will do whatever it takes to support our friends and allies in Belgium and bring to justice those who are responsible.
“The world must unite. We must stand together regardless of nationality or race or faith and fight against the scourge of terrorism.
“We can and we will fight those who stand in the face of security around the world.”
US Democrat leader Hilary Clinton has said in a statement: “Brussels attacks will only strengthen our resolve to stand together as allies and defeat terrorism and radical jihadism.”