The SNP leader admitted the word "national" could be "hugely problematic".
Recorded Crime Falls To 40-Year Low
Crime in Scotland fell to the lowest level since 1974 in the first year of the single police force but sexual offences rose 12%, official statistics show.
There were a total of 270,397 crimes recorded by Police Scotland in 2013-14, down 1% from 273,053 the previous year.
Violent crime dropped 10% to 6,785 while murders and culpable homicides fell to 61 from 65.
Sexual crimes rose by 12% to 8,604, with the force attributing about half of the increase to a rise in the number of victims of historic crimes coming forward.
There was also an 8% rise in the number of sexual crimes solved, resulting in a 76% "clear-up rate''.
After a decrease last year, the number of crimes of death by dangerous or careless driving rose from 19 to 37.
Crimes of dishonesty, such as housebreaking, shoplifting and other thefts, increased slightly during the period, up 1% to 137,324, while drug offences and crimes against public justice also rose 1% to 63,266.
Instances of fire-raising and vandalism fell by 9% to 54,418.
New Justice Secretary Michael Matheson said: "These strong statistics are backed by over 1,000 extra police officers since 2007, protecting the public and keeping communities safe.
"It is clear that I am inheriting a strong record of achievement in justice which I am keen to build on in the weeks and months to come.''
Mr Matheson said he recognised there was still work to do, particularly in relation to sexual crimes.
He said: "We want victims to have confidence to report these crimes.
"The Scottish Government, police and prosecutors take the investigation and prosecution of these traumatic crimes extremely seriously, which is why we have strengthened the law around sex crimes by bringing in the Sexual Offences (Scotland) Act 2009.
"We are giving £3.6 million funding to support victims of rape from 2012-15. Meanwhile, the new national police service has improved investigation techniques, setting up a new national rape taskforce which treats rape as seriously as murder.
"It is also reassuring to see the best clear-up rate for these crimes in a decade.
"Crimes of death by dangerous and careless driving are also up on last year, which should serve as a warning for those drivers who continue to take risks on our roads.
"It is unacceptable, it costs lives and will not be tolerated by our law enforcement agencies.
"Measures to lower the drink drive limit come into force next month and will help make our roads safer and save lives.''
Police Scotland Chief Constable Sir Stephen House said: "The past two years has seen the biggest structural change to how policing is delivered in more than a generation.
"These figures demonstrate that our performance has remained strong throughout that period of unprecedented transition, the number of people becoming victims of crime continues to fall and that those who commit crime are more likely than ever to be caught.''
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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