Manley warned that it was not clear whether any more bombs had been left in place around the city.

The bombings had unnerved residents of Austin, a city of some 1 million people. The first bombings occurred as the state capital was hosting the annual South By Southwest music, film and technology festival.

Police said Conditt had left the hotel in Round Rock, Texas, about 32 kilometres north of Austin, while they were waiting for reinforcements to arrive.

He was followed and later pulled off the city's main highway. As two Austin police officers approached the vehicle, a device exploded. One officer fired at the vehicle and the other sustained a minor injury when the bomb went off, Manley said.

Police urged residents of the area to treat packages with suspicion during the bombing campaign, and Manley warned residents not to let their guard down yet.

"Everybody needs to remember that this investigation is continuing. We still need people to be vigilant," Austin Mayor Steve Adler told the local CBS news affiliate early on Wednesday. "We don't know where the suspect has been the last 24 hours."

US President Donald Trump on Twitter congratulated police, saying, "Great job by law enforcement and all concerned!"

The first three devices were parcel bombs dropped off in front of homes around Austin neighbourhoods. A fourth went off on Sunday night, apparently detonated with a trip wire, and one exploded inside a FedEx Corp facility on Tuesday.

In a memo on Wednesday, FedEx Corp said "key evidence" it had provided to law enforcement officials had led to the identification of the suspect.

"FedEx was able to provide law enforcement with key evidence leading to the identification of the suspect responsible for the bombing because of our advanced security capabilities and the vigilance of our team members," FedEx chief operations officer David Bronczek said in the memo.

FedEx was screening every package at the Texas facility where a parcel exploded on Tuesday, and will also X-ray entire trailers of packages at its sorting facility outside Austin, as well as those originating from or sent to the Austin area, a FedEx manager said.

The series of bombings began on March 2 and bewildered law enforcement officials, who by Sunday began taking the unusual step of publicly calling on the bomber to get in touch and explain why he was carrying out the attacks.

The first two bombs killed black men, raising fears that they were part of a hate crime, but investigators said the later, more random blasts made that less likely.

Manley said investigators still had no clear idea of what prompted the suspect to carry out the bombing.

"We do not understand what motivated him to do what he did," Manley said.

"We don't know if he was on his way to deliver another bomb," Manley said. "He had one with him and that's what he detonated as we approached."

Reuters