The Prime Minister praised the “excellent” work of police and other agencies in driving down knife crime across Scotland, particularly in Glasgow, where the Violence Reduction Unit (VRU) has been praised for its impact.
Mrs May confirmed she will hold a summit in Downing Street bringing together police forces and other agencies to confront the growing crisis.
The government has already said it will consider the public health approach to knife crime that is seen as the cornerstone of Scotland’s success in dealing with the issue.
“The public don't want to see politicians throw blame at one another for these stolen lives,” Ms Lopez said.
“They want to see them take responsibility for what is within their control, provide resources necessary, and then demonstrate a relentless and total commitment to snuffing out violent crime.”
The Prime Minister replied: “We are bringing together ministers, local government, police and other agencies - this needs to be a cross society approach in terms of dealing with this issue, because it’s not just about catching the perpetrators of the crime, it’s about preventing the crime from taking place in the first place.
“That’s why the government will be launching a consultation on treating this as a public health issue.
“There has been excellent work done under what was Strathclyde Police, now Police Scotland, using the public health approach.
“What that does is ensures that all agencies, not just across government, but in local government and elsewhere, are able to be brought together to deal with this issue.
“What I want to do at that summit is hear directly from those [agencies] what other action government can take which we can then put in place to deal with the issue.”
The Prime Minister also clashed with Jeremy Corbyn over the issue, with the Labour leader claiming Mrs May is trying to keep communities "safe on the cheap".
The Labour leader challenged Theresa May to explain if she had any regrets over cutting police officer numbers and criticised the impact of "systematically" stripping away public services to support young people.
Mrs May insisted that “it's a fact more money is being put into the police this year, that more money is being put into the police next year.”
Speaking after emergency talks with chief constables on Wednesday, Home Secretary Sajid Javid pledged to do "everything I can" to provide police with the resources they need to tackle Britain's knife crime epidemic.
Chairwoman of the National Police Chiefs Council Sara Thornton linked the fall in police officers to rising crime.
She added: "It's not the only thing that's going on but it's part of the equation."
Mr Javid said: "I think police resources are very important to deal with this. We've got to do everything we can.
"I'm absolutely committed to working with the police in doing this. We have to listen to them when they talk about resources."