They found the two injured victims: a 17-year-old boy, who later died, and a woman, whose injuries were not thought to be life-threatening.
The first call Monday came at 6:44 a.m.
The 17-year-old found a package outside his house in a tree-lined, mixed race residential area and brought it into the kitchen, where it exploded, Manley said.
The home reportedly received "significant" damage from the blast.
Manley said it is not believed that this third package was left by an official delivery service, and they now do not have any suspect or vehicle descriptions at this time. It was placed on the doorstep in a manner that was similar to another blast this month.
Medics transported a 75-year-old woman to Dell Seton Medical Center after she retrieved an exploding package outside her home. She is said to be in a critical condition.
The second explosion on Monday happened at 6700 block of Galindo Street around noon.
The twin bombings followed an initial blast on March 2, when a 39-year-old man was killed - also after opening a parcel bomb.
Map of Austin package explosions.
Austin Interim Police Chief Brian Manley warned the community not to take any package that is left outside their home inside.
McManus said in a news conference he has been in contact with Manley, who shared that Austin PD has been receiving a lot of calls from people across the city reporting suspicious packages.
Austin resident Trey Mathis said he expected a package to be delivered Monday but was still nervous when it showed up.
The package detonated early Monday.
The incident is being investigated by police and federal authorities, as a homicide, the chief said.
Officials in Austin are responding to another package explosion in the city.
Monday's second explosion occurred around the Montopolis neighborhood, about 5 miles south of the day's first blast. Police have classified the incident as a suspicious death.
"There are similarities that we can not rule out that these two incidents are, in fact, related", Manley said. In reference to speculation that the bombings were a spate of hate crimes, Manley added that investigators haven't identified a "specific victimology or ideology based on current evidence..." We are not going to tolerate this in Austin.
The police chief refused to provide many details about how the explosives were packaged, citing the ongoing investigation. Police said they had no indication it was related to terrorism.
"We don't know what the motive behind these may be", he said. "We have innocent people being hurt".
The attacks took place as Austin hosted thousands of out-of-town visitors for its annual South by Southwest festival.