"We will find you ... You will face justice," said Obama while addressing a public interfaith service honoring the victims of the bombings, which left three people dead and over 170 injured.
Obama paid tribute to the city of Boston, which is still recovering from the shock of the deadly blasts, and called the bombings a "heinous act."
"You will run again," Obama told the Boston audience, adding that the bombers had picked "the wrong city" in their attempt to intimidate Americans.
Twin explosions occurred on Monday afternoon near the finish line of the Boston Marathon, causing heavy casualties. The deceased included an 8-year-old boy, a 29-year-old woman and a 23- year-old female Chinese student at the University of Boston.
The authorities have called the bombings an "act of terror," but the motives and perpetrators remain unknown.