Downing Street has declined to offer support to the Conservative candidate for London mayor, who has been accused of politicising the disappearance of Sarah Everard.
The marketing executive vanished while walking home to Brixton, south London, from a friend's house in Clapham on 3 March.
On Wednesday, a police officer held in connection with Ms Everard's disappearance was arrested on suspicion of murder.
And later that evening, police said they had found human remains in woodland in Kent.
"As a father and husband it breaks me to think that my wife and daughter have to live in fear in their own city," Mr Bailey posted on Twitter before news of the arrest and discovery of human remains were announced.
"It doesn't have to be this way.
"As Mayor, I'll ensure that we are working to deliver for the safety of women and girls in London."
Mr Bailey's tweet was raised at a regular Westminster briefing for journalists.
Asked if the prime minister stood by his party's mayoral candidate, Boris Johnson's press secretary Allegra Stratton said: "You have heard from the prime minister this morning, expressing real shock and distress at what's happened.
"This is a conversation to have with Shaun Bailey. You have seen the prime minister's approach today and you have seen the home secretary's approach today."
Asked again if Mr Bailey had Mr Johnson's backing, Ms Stratton said: "Today, we believe, is a day to give sympathy to the family of Sarah in an incredibly difficult and distressing time for them."
Speaking to Sky News earlier, business minister Paul Scully backed Mr Bailey.
Asked if he could still run for mayor of London, Mr Scully replied: "Absolutely."
Mr Scully, who is also minister for London, continued: "Shaun Bailey has a plan for London in terms of giving the leadership on crime, on housing, on transport and air quality.
"The first thing people want to be is safe in their homes and Shaun has been doing a lot of work around [that].
"But we shouldn't be distracted from the fact that there is a serious crime that's gone on here."
Sky News contacted Mr Bailey for a comment in the wake of his tweet being posted on Wednesday, but has yet to receive a response.
He was swiftly criticised for the tweet after it was posted, with Liberal Democrat mayoral candidate Luisa Poritt posting: "I find it utterly grotesque that @ShaunBaileyUK is politicising the disappearance of a young woman.
"Her disappearance has nothing to do with his campaign and he should apologise immediately."
Catherine West, Labour MP for Hornsey and Wood Green, said: "This is really not the time for cheap, political point scoring."
Matthew Pennycook, Labour MP for Greenwich and Woolwich, said: "The man is utterly shameless."
Dr Rosena Allin-Khan, Labour MP for Tooting, said: "The Conservative candidate for London Mayor is politicising an active investigation into the disappearance of a young woman."