Boris Johnson has refused to back calls for a public inquiry into the murder of Sarah Everard at the hands of serving Met Police officer Wayne Couzens.
The Prime Minister said the Government would "look systemically" at a whole spectrum of violence against women, including the "handling of rape, domestic violence, sexual violence and female complaints about harassment".
But he said probes by the Independent Office for Police Conduct and the Met into the Sarah Everard case must be allowed to conclude.
The PM told the BBC’s Andrew Marr Show: “We do need to look systemically at not just the Wayne Couzens case but the whole handling of rape, domestic violence, sexual violence and female complaints about harassment all together.”
He continued: “We will stop at nothing to make sure that we get more rapists behind bars and we have more successful prosecutions for rape and for sexual violence.
“Because that, I think, is going wrong.”
It comes after 33-year-old marketing executive Miss Everard was raped and murdered by Couzens, after he made a fake arrest.
Couzens was known as 'the rapist' among colleagues and the Met knew he was accused of flashing, but failed to remove him from his post.
Separately, the police watchdog is investigating serving officers who exchanged misogynist and racist messages in a WhatsApp group with Couzens.
Met Police chief Cressida Dick faces calls to resign over the force's handling of the case.
Fury erupted on Friday when the force advised women to flag a bus or call 999 if they suspected an office.
Mr Johnson backed the advice, which also included suggestions to shout or knock on doors.
The PM said: “If you are suspicious about the way in which you are being treated by a police officer and you are worried for some reason, then clearly you should seek help in the way you have described.
“My view is that the police do – overwhelmingly – a wonderful job and what I want is the public, and women in particular, girls and young women, women of all ages, to trust the police.
“They are overwhelmingly trustworthy.”
Meanwhile, Parm Sandhu, ex chief superintendent in the Met Police, said all working cops should be re-vetted and screened regularly.
She told Sky News: "I have real, serious concerns about the vetting procedures.
"This man not only got through the vetting after indecency offences in 2015 and 2018. He was taken to the Met. He was then given a gun to carry on the streets of London, so that was another form of vetting.
"I believe there are other individuals who have got questionable backgrounds, who should be being looked at, not just in the Met, right up and down the country, and I think we have missed that, and instead of looking backwards we should be looking forward and making sure that those individuals are targeted now."
She added: "It [re-vetting] needs to be done now as an urgent measure to reassure the public and rebuild the trust and confidence that policing has lost, but it needs to be done on a regular basis so that we don't have anybody who can even come close to the actions of Wayne Couzens.
"We need to make sure that we restore that trust and confidence."
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