Nick Herbert said that when criminals wear tags equipped with the latest GPS (global positioning system) technology, officers will be able to tell where they are 24 hours a day and so can quickly link them to crime scenes or rule them out of investigations.
He told a conference this morning that the alternative to increasing the use of electronic tags, which he described as a "semi-custodial" option, was to put more people into Britain's crowded jails.
His comments came after a study by Her Majesty's Inspectorate of Probation found that more than half of those given tags instead of prison sentences are breaching the terms of their orders, and are able to go missing for 11 hours and 59 minutes of a 12-hour curfew yet escape with a mild warning.
Basic errors are also being made on important forms while it was "deeply worrying" that a man known to commit domestic violence was ordered to remain at home with his wife, who he went on to attack.
A separate dossier compiled by the probation union Napo claimed that the ankle bracelets themselves are prone to breaking in baths or remote areas, and called for a review of the entire £100million scheme before it is expanded to include round-the-clock monitoring for up to 180,000 offenders.
Mr Herbert was told at the Policing 2012 event in Westminster by a Napo official that tagging is a "shambles" and that the Government is "wasting millions upon millions on a system that palpably does not work".
"I think that it's perfectly legitimate to look at the practice of electronic monitoring and to ensure that we have a robust use of it, that's important for public confidence.
"But I don't think we should dismiss the existing programme of electronic monitoring or the potential for more advanced use with satellite tracking.
"This has huge potential to prevent crime and ensure more effective supervision of offenders."
The minister said police in Washington DC are already using satellite tags to pinpoint offenders' locations at all times of the day, and claimed it helped detect crime as well as keep tabs on people.
"It was immediately clear whether someone who was being tracked was - or indeed was not - somebody who should be treated as a suspect in relation to the commission of an offence."
It could also rule out potential suspects if the tag showed they were at home and nowhere near a crime scene.
"I think that the opportunity which this technology has is very great and satellite technology in particular enables the development of semi-custodial options, and the alternative of course is they we'd have to resort to more custodial options. Does anybody really want to have that?
"Where we can have the effective use of technology for the supervision of offenders, including some high-risk offenders, than would otherwise be allowed by human processes, or would require us to resort to more custody - and we already have a record prison population in this country - then it must make sense to use it."
Earlier the Home Secretary, Theresa May, said the findings of the HMIP review would be examined "seriously" and changes made if problems continue to arise.
She told BBC Breakfast: "This report from the Chief Inspector will be looked at very seriously but the Ministry of Justice has already been looking at the way that it tags people and at new contracts for tagging.
"It's already been looking at how this system works and what the newest technology is that's available in order to make sure that we can do what we want to do with tagging, which is important."