BRUSSELS—Belgian police continued to search the country Wednesday for the terrorist who escaped from one of two areas hit by explosions in the capital the previous day in which more than 30 people were killed.

Brussels was brought to a standstill Tuesday after a pair of bombs hit the city’s airport and a third explosion struck a subway station near its European Union institutions. Islamic State claimed responsibility for the attacks.

Belgium’s health minister, Maggie De Block, told VRT radio that “about 31” died, and “almost 260” were injured in the attacks, warning that the number may go up soon.

Belgian police on Tuesday night searched what officials said was the home of the suspected airport attackers. Prosecutors said they would release more information later Wednesday.

Meanwhile, the threat level for all of Belgium was kept at four out of four. “‘Level 4’ means that there continues to be a real threat and that we request everybody to stay vigilant,” the country’s Crisis Center said.

Police were searching for a man who appeared in a surveillance photo taken at the airport moments before the blasts along with the two alleged attackers who died in the explosions.

The two men who died in the blasts wore dark tops and, crucially, dark gloves on their left hands, which may have allowed them to hide detonators for explosives.

The man who is still on the run didn’t wear any gloves and was mostly dressed in light colors. A dark floppy hat partially obscured his face.

The different attires worn by the three alleged airport attackers may be a sign that they came to the site of the attacks with different purposes, two of them as suicide bombers and one intending to escape.

Police also continued to search for Najim Laachraoui, a Syrian-trained fighter who Belgian authorities identified on Monday on suspicions of ties to the Paris attacks last November. Police haven’t said whether Mr. Laachraoui was involved in Tuesday’s attacks.

French investigators believe Mr. Laachraoui was involved in the construction of the suicide vests that were detonated in the Paris attacks. His DNA was found on some of the suicide vests used in Paris as well as the Brussels apartment Belgian authorities have said were used to make those bombs.

On Monday, Belgian authorities asked for the public’s help in finding him.

Didier Reynders, the Belgian foreign minister, said Wednesday that Brussels was a target because it is a European and trans-Atlantic symbol, as host to the EU and North Atlantic Treaty Organization. Mr. Reynders said there were likely more than 40 different nationalities among the victims.

“It probably wasn’t by chance that the attacks took place in an international airport and in a metro station very close to the European institutions,” he said.

The U.S. State Department put out a travel alert, citing the Brussels attacks and warning of potential risks. “Terrorist groups continue to plan near-term attacks throughout Europe, targeting sporting events, tourist sites, restaurants, and transportation,” the alert said.

French Prime Minister Manuel Valls warned that the terror threat was at its highest-ever level in France and that authorities shouldn’t rule out the possibility of a chemical-weapons attack.

A day after the attacks, life was anything but normal in Brussels.

Fear continued to rest heavily and a sense of disorder pervaded the city. Some normally busy streets were empty, blocked by police. Others were jammed with traffic, a sign of people trying to get about a normal day.

Many metro lines, trams and buses resumed operating but with altered schedules. Security services were checking people accessing underground transport, including metros and some tram stations. The airport was closed but authorities said they would decide later in the day when to reopen after assessing the damage to the terminal.

Several schools reported that many children were being kept home by parents.

At a high school in the residential neighborhood of Ixelles, only around half of the students had shown up by 8:30 a.m., according to co-principal Marie-Aline Dath.

Ms. Dath said many students normally get to school by subway. The mood was calm, even as sirens undercut the otherwise quiet streets around the school.

“It won’t be a normal day,” said Ms. Dath.

Belgian authorities warned over the weekend that follow-on attacks were possible and stepped up patrols in Brussels. Still, the police weren’t able to prevent Tuesday’s explosions, and criticism of Belgium’s ability to hunt down and arrest radicals before they attack is rising.

Speaking on one of Belgium’s public broadcasts, Jan Jambon, the justice minister, defended the country’s police work.

“We know very well we have the highest number of foreign fighters [per capita]—that’s the truth,” he said. “I think we are doing what is necessary—but 100% guaranteed security, no one can grant that.”

The police presence remained high around the city.

At the Ixelles school, a police officer had stood guard over the arrivals and Ms. Dath and another teacher were greeting students.

Some of the teachers had stayed at the school until 6 p.m. Tuesday to wait until parents were able to pick up their children. News of the attacks had spread quickly through the school, said Ms. Dath.

“The moment one of them knew, all knew,” she said.