In an interview with ITV News, Christopher Jefferies said the letter of apology from Avon and Somerset Police was the "equivalent" to apologies he received from a number of newspapers.
Mr Jefferies added that the apology acknowledges "distress" caused not only to him, but friends and members of his family.
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Voting that had been expected on Thursday will now be held Friday instead.
Police were called in amid fears the man may have been poisioned.
Williams is charged with first-degree murder without premeditation, a probation violation and for not having a valid driver’s licence.