Glasgow's Lord Provost Sadie Docherty was the first signatory of a book available in the City Chambers foyer. The pages are situated beneath a plaque commemorating the 30th anniversary of Glasgow awarding Mandela the Freedom of the City, and which was unveiled by Denis Goldberg in 2011, a fellow defendant at the now-infamous Rivonia trial.
In Edinburgh, members of the public will be able to sign a book in the City Chambers between 7am and 7pm for the next seven days, or leave a message via the council website.
Lord Provost Donald Wilson, who was first to sign the book, said: "I would encourage people to sign the book of condolence and to reflect upon his great courage, strength and determination. His legacy and everything it represents will live on for generations to come."
The Lord Provost has submitted a motion to next week's council meeting calling for a report that explores how Edinburgh can create a lasting tribute to Mandela.
South Ayrshire Provost Helen Moonie was the first to sign the book of condolence and paid tribute to Mandela, saying: "Nelson Mandela was an iconic and inspirational leader, who touched millions with his simple message of peace and forgiveness. He has a special place in our hearts and was a kindly, fatherly figure to the nation of South Africa - a unifier who brought an end to apartheid and saved his homeland from civil war.
"His message was simple and powerful - peace, forgiveness and tolerance must flourish over hatred, bitterness and bigotry and he never lost sight of those principles."