Earlier Yudhoyono's spokesman told Al Jazeera the president had been briefed by the heads of the Indonesian police, security and intelligence agencies and had vowed that the perpetrators of the bombings "will be punished, and punished hard".
Andi Mallarangeng said police had already begun gathering clues and evidence at the scene and elsewhere, although he said it was "too early" to say who may have been behind the attack.
Yudhoyono, who secured a second term in presidential elections last week, has been credited with bringing several years of peace and stability to Indonesia after a spate of bombings and other attacks.
However, Mallarangeng denied suggestions that authorities had let their guard down.
"In five years we have had a very good record on security," he told Al Jazeera.
Mallarangeng described the bombing, which left at least nine people dead and dozens injured, as a "cowardly" attack on humanity.
"There's no way we are relaxing – our record shows we have arrested terrorists or anyone suspected of terrorist activities. But these cowardly people found a way to hit back."
Nonetheless, Mallarangeng said, the government would be reviewing all levels of anti-terrorist activity.
The attackers, he said, were the common enemy of all civilized people of the world.
"Our security officials are working all day to make sure that these people are punished and we will destroy any possibility of activities like this."