Mr Salmond passed away on Saturday while he was in North Macedonia at a conference.
Mr MacAskill, who was East Lothian’s MP from 2019 until earlier this year, said that it would “take us all time to process his sudden loss and it is right that we do so”.
The politician, who was elected as East Lothian’s MP as the SNP candidate before switching to Alba in 2021, said of his close friend: “He was the outstanding Scottish politician not just of his generation but for generations far before.
“Recognised at home and respected abroad, he was not just a master political tactician but strategist, yet also a politician who was a superb debater and orator, but one who equally possessed extraordinary charm and a common touch which endeared him to so many in Scotland.
“His record speaks for itself in moulding the modern SNP, forming the first independence administration and delivering both an unprecedented Holyrood majority and a referendum on independence.
“His legacy lives on and has benefitted Scotland immensely with infrastructure and other social and economic gains testifying to that.
“A family has lost a husband, a brother and a much-loved uncle. I have lost one of my oldest and dearest friends.
“The party grieves the loss of their founder and leader.
“Across Scotland, people are mourning the loss of their former First Minister.”
Morgwn Davies, of Alba East Lothian, said that the group had been “shocked” when they heard the news.
He added: “It was hard when the news broke to accept the truth that Alex was no longer with us.
“Since Saturday, we have been coming to terms with the loss of our party leader and the best First Minister Scotland has had.
“Our thoughts have been with Alex’s wife Moira, his extended family and his many, many close friends who will feel the loss so keenly.
“We will take time now to grieve but, in time, we will ensure that the ALBA Party will continue and we will redouble our efforts to ensure that the dream, and desire for re-establishing Scottish independence, will be fulfilled.”
