The National Highway Traffic Safety Administration and National Transportation Safety Board both sent two "full teams" of people to the city, police said.
"They want to understand what has happened here and the technology in place," said Tempe Police Commander Jeffrey Glover.
He expects the teams to assist Tempe's traffic investigation and do their own investigations.
The NTSB published a news release on Monday saying the probe would "address the vehicle’s interaction with the environment, other vehicles, and vulnerable road users such as pedestrians and bicyclists."
Chief investigator Jennifer Morrison will lead three NTSB investigators "who will examine vehicle factors, human performance, and electronic recorders," the agency said.
Uber sent a team of people from its corporate headquarters on Tuesday as well, Glover said.
The San Francisco-based company halted its self-driving-car test operations in Phoenix, Pittsburgh, San Francisco, and Toronto after the collision. Until then, then sometimes-autonomous Volvo XC90 SUVs were a common sight in Tempe, often grouping together in twos or threes at intersections near Arizona State University.
One of those vehicles was driving north on Mill Avenue at about 10 p.m. on Sunday when it hit a woman pushing a bicycle laden with shopping bags across the street. She later died at a local hospital.
The Volvo was in the lane nearest the curb, about 100 yards south of Curry Road, and going about 40 mph at the time of the collision. Initial evidence shows the vehicle didn't brake "significantly" before the impact.
Tempe police said on Monday, and Uber later confirmed, that the Volvo was in "autonomous mode" when it struck 49-year-old Elaine Herzberg. An Uber backup driver, Rafaela Vasquez, was in the driver's seat at the time.
On Monday, Tempe police Sergeant Ronald Elcock told reporters that impairment doesn't appear to be a factor for either Herzberg or Vasquez, and that it was too early to tell who was more at fault. He declined to characterize the statements Vasquez made to police after the crash.
Tempe Police Chief Sylvia Moir, who was chief of police in El Cerrito, California, before becoming Tempe's chief in March 2016, went into greater detail with the San Francisco Chronicle on Monday.
She said Vasquez told police "it was like a flash; the person walked out in front of them."
"(Vasquez's) first alert to the collision was the sound of the collision," Moir told the newspaper.
Moir said that after watching video from the Uber car of the moment before the collision, "it’s very clear it would have been difficult to avoid this collision in any kind of mode (autonomous or human-driven) based on how she came from the shadows right into the roadway ... I suspect preliminarily it appears that the Uber would likely not be at fault in this accident."
Glover downplayed Moir's statements, saying some were taken "out of context" by the Chronicle. The chief disagrees with the Chronicle's headline, "Tempe police chief says early probe shows no fault by Uber," Glover said.
Moir, who did not return messages from Phoenix New Times on Monday or Tuesday, told the Chronicle that she would not rule out seeking charges on Vasquez, if the investigation warrants such an action.
Maricopa County Attorney Bill Montgomery's office will decide if any laws were broken. If there are criminal charges, the case seems likely to break new ground in technology law.
If Vasquez is charged with a crime, Uber likely will provide serious legal help. It's also possible, according to Governor Doug Ducey's office, that Uber as a corporate "person" under the law could be criminally charged in the right circumstances.
Ducey's office invited Uber to the state in 2015 with the promise of fewer rules. On March 1, following questions about the lax rules and the possibility of no-backup-driver testing, Ducey issued a new executive order with slightly more stringent requirements.
Uber's one of several companies conducting testing of self-driving technology in Arizona.
See below for Tempe PD's news release on the federal agencies' investigation of the Uber crash: