Paul Robson, who is serving a life sentence for attempted rape and indecent assault, was reported missing from HMP North Sea Camp near Boston at about 7am on Sunday (February 13).
Police urged the public not to approach the 56-year-old as he "can cause real harm to anyone he comes across".
Det Chief Supt Andy Cox said: "We are still working tirelessly to locate Paul Robson and are still working through numerous lines of inquiry.
"He could be anywhere in the country, and we are really keen to hear from the public with potential sightings so we can take this man off our streets."
The prisoner, who walked out of HMP North Sea Camp, is described as a white male with a bald head, a long goatee beard and is of a slim build.
"Robson is a dangerous sex offender and while he presents a particular danger to women and young children, I believe he can cause real harm to anyone he comes across," Det Chief Supt Andy Cox added.
"If you see Robson, please do not approach him, and do not try to apprehend him yourself. Call 999 immediately."
Labour said Justice Secretary, Dominic Raab, has "serious questions to answer" following the Government's decision to deem Robson fit for the open prison following a Parole Board recommendation in February last year.
During his fifth parole review, Robson was refused release but recommended for a move to the Category D open prison.
The Newcastle-born sex offender was jailed at Oxford Crown Court in 2000 after he entered a woman's home through a cat flap before tying her up, putting a pillow case over her head, and brutally assaulting her while holding a knife to her throat.
He was handed a life sentence with a minimum term of nine years but has spent an additional 11 years in prison.
Robson had only been released from prison three weeks before the attack and was on licence - with the sentencing judge describing him as a "menace to females".
Commenting on Robson's case, a spokesman for the Parole Board said: "The Parole Board refused the release of Paul Robson but recommended a move to an open conditions prison following an oral hearing in February 2021.
"This was a recommendation only and the Secretary of State for Justice considers the advice before making the final decision on whether a prisoner is suitable for open conditions.
"We will only make a recommendation for open conditions if a Parole Board panel is satisfied that the risk to the public has reduced sufficiently to be manageable in an open prison.
"A move to open conditions involves testing the prisoner's readiness for any potential return into the community in future. Prisoners moved to open conditions can be returned to closed conditions if there is concern about their behaviour."
HMP North Sea Camp is a category D men's open prison which holds a large proportion of sex offenders and those serving indeterminate sentences, according to an inspector's report following a scrutiny visit in April last year.
The report, published in June, said 70 per cent of prisoners were assessed as "presenting a high risk of harm to others" and more than half were convicted of sex offences.
After writing to Mr Raab about Robson, the Shadow Justice Secretary Steve Reed said: "Dominic Raab has serious questions to answer about why such a dangerous criminal was deemed fit to be in an open prison where he could abscond.
"The public will be deeply concerned that, yet again, this high-on-tax, soft-on-crime Conservative Government have put the public at risk."
Police have urged anyone with information or confirmed sightings of Robson to call 999.
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