The SNP leader admitted the word "national" could be "hugely problematic".
Judy Murray Gets Glasgow Uni Honour
The mother of tennis stars Andy and Jamie Murray said she hopes to use her sons' success to build the sport across Scotland.
Judy Murray made the comments after being awarded an honorary degree from Glasgow University in recognition of her contribution to tennis at both grassroots and professional level.
She added: "I was the Scottish national coach for 10 years and when I took the role there was no track record of any success of tennis in Scotland.
"In fact, when I took the role on we only had one indoor centre in the whole of the country, so we were starting pretty much with a blank canvas and managed to produce four Davis Cup players, one Fed Cup player and obviously some grand slam titles and some Olympic gold and silver, so it's enormously raised the profile of tennis in Scotland.
"I'm trying to use that profile that Jamie and Andy, in particular, have created, the success they've had on the world stage, to really build the game at grassroots level.''
The 56-year-old was named a doctorate of the university and said she was ``absolutely thrilled'' to be one of 22 people being honoured at a ceremony on Wednesday.
She added: "It's a really special day, the whole thing, the whole ceremony, and the fact that there were 22 people getting honorary degrees today and everyone has done something very special in completely different fields. It was wonderful to hear all the stories.''
Scottish rugby stars Alastair Kellock and Gregor Townsend were given a joint doctorate of the university for their contribution to rugby and community engagement as the former captain and current head coach of Glasgow Warriors.
They said they were "surprised'' to be nominated and ``hugely honoured'', with Kellock saying he felt ``humbled'' by the talent of the others being recognised on the day.
Townsend added: "There was a speech in the ceremony talking about Glasgow University being the city's university and I feel the same way about the Warriors team.''
Fellow former Scotland player John Beattie, former Solicitor General for Scotland Lesley Thomson QC and the university's Professor Jim Hough, who fulfilled his lifelong quest to discover gravitational waves, were among the others receiving honorary degrees.
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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