Sex offender Peter Tobin was missing when he murdered Angelika

The Tories hope to get cross-party support for high-tech tracking devices to monitor their movements.

The SNP-run executive said it was open to new proposals.

Tory justice spokesman Bill Aitken expects to meet First Minister Alex Salmond and Justice Secretary Kenny MacAskill in the coming weeks.

The Tories want the photographs of those sex offenders who vanish and go underground to be published.

Mr Aitken said tracking devices would allow then to trace offenders more quickly if they went missing.

In addition the Conservatives are calling for offenders who have gone on the run to undergo lie detector tests after they have been caught, in a bid to discover what they have done.

Something should be done in respect of the operation of the sex offenders register, which is not working as we would have hoped Bill Aitken Tory justice spokesman

The meeting with Mr Salmond and Mr MacAskill is to take place after it emerged that Peter Tobin, the convicted sex offender who raped and murdered the Polish student, had been on the run for almost a year before he killed her.

Tobin, 60, vanished from his Paisley home in October 2005 following an incident involving a young woman.

Officers found him 11 months later - but by that time Tobin had killed Miss Kluk and hidden her mutilated body under the floor of Glasgow's St Patrick's Church.

Last week the killer, who is serving a life sentence with a minimum of 21 years behind bars, was handed a further 30-month sentence for breaching the terms of the sex offenders' register.

Mr Aitken said: "I think the majority view in the parliament is that something should be done in respect of the operation of the sex offenders register, which is not working as we would have hoped.

"I think the vast majority of MSPs agree with that and I am hopeful that changes can be made."

Mr Aitken said: "We will never know if these changes would have prevented Angelika Kluk from being murdered.