Officers in Austin spoke about the attacks following two explosions on Monday.
Just hours after a package bomb killed a teenager and wounded a woman, police were called to deal with another blast elsewhere in the city.
Detectives are linking the incidents to a similar bombing in the city earlier in March, in which a 39-year-old man was killed.
They are investigating whether the bombings were racially motivated as all the victims are black.
Mr Manley told reporters after the latest blast on Monday: “Based on evidence that we have at this scene, as well as at the other two scenes where we’ve had these explosions, this evidence makes us believe that these incidents are related.”
Mr Manley had earlier tweeted: “My heart goes out to the family of the individual who died and was injured from the explosion in Old Fort Hill. This type of crime will not be tolerated in ATX.”
It comes as hundreds of thousands of visitors descend on the city for the South By Southwest music, film and technology festival.
Officials have urged the public to call police if they receive any packages they are not expecting.
The three explosions occurred in different areas in the east of the city.
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The first explosion on Monday happened at a home near the Windsor Park district, and about 12 miles from the home where the first explosion, on 2 March, killed 39-year-old Anthony Stephan House.
The first blast was first thought to have been a suspicious death but is now being treated as murder.