Mr Duncan Smith expressed concern over crime
The prime minister's comments came just hours after a Downing Street summit on crime and as the government's record came under fire in the House of Commons.
The Commons exchange came as the head of Avon and Somerset police, Steve Pilkington, warned that the nation was on the verge of a crime epidemic fuelled by crack cocaine use.
Mr Duncan Smith said: "Isn't it true that because of Labour's failure to tackle crime and bring it down on the street, criminals now don't need to run from the scene of a crime, they only need to walk."
But Mr Blair responded by saying that crime under the last Tory government had doubled while under Labour it had fallen.
'Under control'
"There are now record numbers of police officers in the country," he said.
"I'm sorry you think nothing is being done on street crime - over the past few weeks, as a result of the Metropolitan Police's safer streets initiative, street crime has fallen."
Mr Blair acknowledged that tackling the issue would be difficult, however.
Later the Conservative leader wrote to the prime minister demanding a justification for Mr Blair's claim that street crime would be brought under control by the end of September.
He also demanded to know why the term "COBRA" was used by officials to describe the crime summit from where the September deadline had originated.
'Major development'
COBRA is usually used as a shorthand for meetings to discuss national emergencies although on this occasion Number 10 insisted the word was merely used to describe the room in which the crime summit took place.
Mr Duncan Smith wrote: "I believe that the last three times [COBRA] met was for the fuel crisis, foot-and-mouth and the war on terrorism.
"Does this now mean that your government accepts that we have a major crisis with the rising levels of street and violent crime and that the police are unable to deal with this on their own?
"I believe that this is a major development."
But Number 10 played down what it said was merely the fourth meeting of the Street Crime Task Force which was held in Cabinet Office Briefing Room A - COBRA.
'Drug-fuelled criminality'
It is not just London which has been hit by rising street crime - a report to be presented to the Avon and Somerset Police Authority shows overall crime there spiralled by almost 20% in the past year.
The report said last summer saw a "major turning point" when crime started to increase sharply following an eight-year fall in the area.
The report highlights the major contributing factor as an increase in "drug-related criminality", fuelled by heroin and cocaine supply by organised crime.
Another element was that the surge in major crime was diverting resources from smaller incidents.
Mr Pilkington said: "There was a serious suggestion that the crack cocaine problem that swept the United States would come to the UK and it didn't really come.
"I have to speculate now as to whether that problem has really reached our shores."
Mr Pilkington said Bristol was not unique and three out of four police forces across the country were experiencing similar problems.
He also said the government was not doing enough to stop smugglers at the UK's ports and airports.