He said it would ensure effective CCTV coverage in mortuaries.
He also said Justice Secretary Dominic Raab is investigating whether the penalties available for such "appalling" sexual offences are adequate.
The maximum sentence for sexually abusing a dead body is two years.
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David Fuller, 67, admitted murdering and then sexually assaulting two women in Kent before carrying out dozens of sex attacks on corpses in mortuariesHealth Secretary Sajid Javid appointed NHS executive Sir Jonathan Michael to lead the probe