He regretted the distorted information being spread about bombs also exploding in several other parts of Jakarta.
Budi stated that the security authorities have intensified early detection measures.
He urged the public to not be easily provoked by terror incidents.
President Joko Widodo (Jokowi) has ordered a thorough investigation into the attack.
The head of state has urged every party to not engage in speculations before the investigation is completed, according to the spokesman.
Jakarta Governor Basuki Tjahja Purnama (Ahok) remarked that the condition in Jakarta is safe.
"Jakarta is safe, do not worry. Yes, the security authorities have tackled it. I also think that this time, there is no more tolerance for such matters," Ahok emphasized.
Seven people were killed in the terror attack, including five of the suicide bombers. A Canadian national and an Indonesian civilian also died in the attack.
Twenty people, including five police officers, were injured in the terror attack.
Following the attack on Thursday, President Jokowi condemned the bomb blasts targeting the Thamrin Boulevard in Central Jakarta and has ordered the police to arrest the perpetrators.
"I have ordered the National Police chief and the coordinating minister for political, legal and security affairs to chase down and arrest the suspects, both those on the scene and other members of the networks," President Jokowi said.
The head of state expressed condolences over the casualties resulting from the blasts.
He affirmed that terror attacks would never be able to incite a sense of fear or defeat among Indonesians and has appealed to the public to remain calm.(*)
Editor: Heru Purwanto
Copyright © ANTARA 2016