Police have defended their decision not to chase an escaped sex offender into a north Queensland river, as the hunt for the fugitive enters a third day.

Tyronne Speechley, 25, and Algana Tiers, 26, were in community supervision under the state's Dangerous Prisoners (Sexual Offenders) Act when they fled a Townsville prison precinct on Monday night.

Tiers was caught at Pallarenda in the city's north yesterday morning and remains in police custody.

Speechley ran into a river and escaped from police, who opted not to go into the water.

Police now say they believe Speechley has since stolen a car in the suburb of Pallarenda overnight.

They think the vehicle he may have stolen is a blue Hyundai hatchback, reported missing from a house near bushland searched by officers.

Authorities are asking any who sees the vehicle to contact police immediately.

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The Queensland Police Union (QPU) says officers could have drowned or been attacked by a crocodile if they had followed Speechley into the river.

"It is known to contain crocodiles, be quite deep in parts, and on top of that, with all the equipment that police have on them at the time, there is a very real risk they will damage or lose their firearms, Tasers, police radios," QPU president Ian Leavers said.

"As well, that equipment may weigh them down and they may very well become the subject of drowning themselves."

Police have patrolled the Townsville suburb throughout the night and urged residents to remain vigilant and secure their homes.

Officers say residents must not approach Speechley and call Crimestoppers on 1800 333 000 if he is seen.

Tyronne Speechley (L) remains on the run while Algana Tiers was apprehended at Pallarenda. ( Queensland Corrective Services )

Mr Leavers says the Corrective Services Department must explain how the two sex offenders managed to escape from the prison precinct.

The men were in community supervision under the Dangerous Prisoners Act.

They were wearing GPS tracking equipment but broke off their tags when they escaped.

Mr Leavers says the men should have been locked up at a secure site.

"All people - women, children and all victims - deserve to be protected from sex offenders - not allow [offenders] to be on prison farms where they can walk away at any point in time," he said.

"Then as we know only too well, [they] will call the police when they escape, and then it becomes the police's problem.

"We need to protect the community and police have a very difficult job as it is."

A Corrective Services spokesman says the Supreme Court determines where offenders are kept.

Police Minister Jack Dempsey says he is looking at stiffer penalties for offenders who cut off GPS tracking bracelets.

"What we're looking at and I'm discussing with the Commission of Corrections, is introducing a mandatory, more severe, sentence of possibly up to 12 months for a person who breaks their bracelets when they're on one of these orders," he said.

Mr Dempsey says he is also concerned about the time it took authorities to warn the public of the escape.

"Obviously two-and-a-half-hours - I'm not happy with that," he said.

"I'll be getting a full briefing with the Corrections Commissioner about this matter."