The home secretary said he wanted a "legal duty" on government departments to help prevent serious violence.
Chairwoman of the National Police Chiefs' Council Sara Thornton said the discussions had been "really constructive "and highlighted the need for extra police officers".
It comes after the fatal stabbing of 17-year-old Jodie Chesney in an east London park on Friday night in what her family branded a "totally random and unprovoked attack".
Two-thirds of police forces in England and Wales recently responded to a Freedom of Information request from Channel 4's Dispatches which showed that, in those force areas, the number of teenagers recorded as having killed with a knife had risen from 26 in 2016 to 46 past year.
Mrs May served as home secretary between 2010 and 2016 and oversaw a period where cuts were made to police forces.
Prime Minister Theresa May has ordered an urgent set of ministerial meetings to address action against knife crime, amid controversy over her claim that there was no direct link with cuts in police numbers.
Seventeen-year-olds Jodie Chesney, who was a scout, and Yousef Ghaleb Makki died at the hands of knife attackers in separate incidents over the weekend.
Lancashire Police said five people had been arrested on Monday after a group of men walked into the grounds of a college carrying knives and threatening students in what was described as a "targeted attack".
He said: "Does the Prime Minister now regret cuts in police numbers and will she undertake that under this review they will be restored to the level they were formerly at?"
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The army could form part of the police's push back against the problem of knife crime, according to Metropolitan Police commissioner Cressida Dick.
South Yorkshire Police attended a meeting with Home Secretary Sajid Javid today as concerns of a national knife crime emergency grow.
"We have a Justice Secretary who is saying we need to scrap shorter sentences because the prisons are full".
Knife crime is on the rise nationally and there were eight fatal stabbings in South Yorkshire a year ago, although locally knife crime is down by 12 per cent.
He told Sky News that online retailers have a role to play in stopping people young people buying knives.
He said: "I think that stop-and-search is a very valuable tool and some police forces have started in recent years making even more use of that, and they have my full support".
But Donna Murray-Turner, who chairs the Croydon Safer Neighbourhood Board, does not believe more police officers will solve the issue.
May, however, has rejected any "direct correlation" between falling police numbers and violent crime, despite the head of London's Metropolitan Police Service suggesting there was "some link" between the two developments.