The attack yesterday was one of the deadliest on security personnel in recent years in one of Colombia's most important cities.
It comes as the government of President Juan Manuel Santos seeks to bring the armed conflict that has wracked Colombia for 50 years to an end. Much of the violence has been financed by drug trafficking.
The bombing also casts a pall over preparations for the annual carnival, a major attraction in the Caribbean port city.
One suspect was captured, he said.
A police source told AFP that 49 officers were at the site when the bomb exploded. Of those, four were killed and 42 were wounded.
The toll is considerably higher than the initial figure of 17 wounded and three killed given by Botero.
Barranquilla Mayor Alejandro Char quickly blamed drug traffickers for the attack.
"I do not have the slightest doubt that this is a retaliation" for successful police action against drug traffickers, he told reporters.
Colombia is the world's top producer of cocaine, and criminal groups have flooded the country's main cities with drugs in a move known as "microtrafficking."
El Heraldo, the main Barranquilla newspaper, said that some believe the attack may have been aimed at distracting police from an armoured car robbery that took place at the same time.
The head of Colombia's national police, General Jorge Nieto, said he travelled to Barranquilla to offer his support to the blast survivors and their relatives.
He also announced a reward of 50 million pesos (USD 17.8 million) for information about the attack.
President Juan Manuel Santos blasted the "cowardly attack" on Twitter.
"We will not rest until we find those responsible, my solidarity with the families of the victims and the wounded," Santos wrote.
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