"Indian boxing reaching such heights in the last few years was largely his contribution. We will miss him dearly. Boxing will miss him. Indian sport will miss him.
"Rest in peace my dear friend. We will always be proud of you," Singh said.
Sports Minister Kiren Rijiju also expressed grief over the veteran's demise.
"Our beloved R K Sacheti ji, Boxing Federation ED has lost the battle against COVID-19. He was one of the pillars who put India in the league of world's top Boxing nations. I wish he could see our Boxers in Olympics.
"I extend my condolence to his family for the monumental loss," he tweeted.
The Indian Olympic Association (IOA) also offered condolences.
"Deeply saddened to hear about the sudden demise of IOA Associate Joint Secretary, BFI Executive Director and dear friend Sri Raj Kumar Sacheti," IOA Secretary General Rajeev Mehta said in a statement.
Sacheti first became BFI ED in 2016 and retained the position after incumbent President Ajay Singh was re-elected in the federation elections held earlier this year.
"...his contribution to the Olympic, and Commonwealth movement in India is fondly remembered," Mehta said.
Last year, Sacheti was invited by the International Olympic Committee's Experts Group to "advise" on the formulation of rules for Olympic Qualifiers."
The Athletics Federation of India (AFI) too mourned the demise of the seasoned administrator.
"AFI family is truly saddened with the news of passing away of Mr. RK Sacheti, Asso. VP AFI, due to Covid. I have known him for over 30 years. He was part of so many major sports events in India & gave opportunity to many youngsters to work in sports industry," AFI President Adille Sumariwalla stated.
Former BFI secretary general Jay Kowli said "sports world has lost an efficient administrator."
"Remembering all the great moments together. Many thanks for all your contribution to Boxing, RKS," Kowli said in his condolence message.