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The prime minister has said he was "concerned that private information was put into the public domain" by police investigating the disappearance of Nicola Bulley.
Rishi Sunak told broadcasters that he was "pleased the police are looking at how that happened".
"The focus must be on trying to find her," he added.
Lancashire Police was criticised for making her struggles with alcohol and the menopause public.
Speaking to Times Radio, Sir Keir Starmer - the leader of the Labour Party and former director of public prosecutions - said he was "very surprised to see what the police had put out there".
"I was not sure why that degree of personal information was necessary," he added.
The home secretary has also raised concerns with police after they revealed personal information about the missing mother of two.
Speaking to the BBC, Mr Sunak said: "Well, I agree with the Home Secretary and like her I was concerned that that private information was put into the public domain and I believe that the police are looking at how that happened in the investigation.
"Obviously my thoughts are with Nicola's friends and family."
Ms Bulley, 45, disappeared three weeks ago during a riverside dog walk in St Michael's on Wyre, in Lancashire, after dropping off her two daughters at school.
Her phone was found still connected to a work conference call.
Lancashire Police said it would conduct an internal review into their investigation, which would be led by its head of crime Det Ch Supt Pauline Stables.
Earlier the information commissioner John Edwards said personal details should not be "disclosed inappropriately".
Home Secretary Suella Braverman spoke on Friday to the Chief Constable of Lancashire Police, Chris Rowley, and his senior team, BBC News has been told.
She "outlined her concerns over the disclosure of Ms Bulley's personal information and listened to the force's explanation", a source close to her said.
She also asked to be kept updated on the investigation, the source added.
In a statement released on Wednesday, Lancashire Police said Ms Bulley had suffered with "some significant issues with alcohol" and "ongoing struggles with the menopause".
This prompted a backlash from campaigners, MPs and legal experts, with some accusing the police of breaching her privacy.
Ms Bulley's family later released a statement via the police, in which they elaborated on her health, saying she had suffered significant side effects due to the perimenopause, including "brain fog" and "restless sleep".
They also asked for speculation surrounding her private life to end and urged the public to focus on finding their "wonderful daughter, sister, partner and mother".
The Independent Office for Police Conduct (IOPC) said it had received a referral from the force regarding the contact officers had with Ms Bulley on 10 January, 17 days before she went missing.
Health professionals also attended her address, the force said, adding no arrests were made but it was being investigated.
Dame Vera Baird, the former victims' commissioner for England and Wales, told BBC Radio 4's Today police had been subject to "heavy, and in my view, totally justified, criticism".
"If it was relevant, it needed to be in a public domain at the start, and it wasn't," she said.
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