The president appears to be recovering well from his undisclosed illness as he's meeting with governors this week.
In a press release signed by the president's Special Adviser on Media and Publicity, Femi Adesina, the president expressed his gratitude for the gesture and assured Conde that he was getting better.
In the letter dated July 24, 2017, Buhari wrote, "I thank you for your kind and thoughtful action in organising nationwide prayers for my good health. It is a gesture that I will forever cherish and treasure.
"Your Excellency will be pleased to hear that I am making good progress, and as soon as the doctors advise, I shall return to my duties and continue serving the Nigerian people who elected me and are daily praying for my recovery."
The press release also stated that the two Africans had earlier talked in a phone conversation.
President Buhari left Nigeria on May 7 to resume treatment in London for an undisclosed illness.
On Sunday, July 23, pictures emerged of the president sitting down at a table to have lunch with governors from his All Progressives Congress (APC) party.
Imo state governor, Rochas Okorocha, who was part of the team of governors, said the president would return to the country soon.
The press statement also indicated that the president had written an earlier letter to accept his nomination as the leader of the "2018 AU theme on the fight against corruption".
The nomination came from African leaders at the 29th session of the Assembly of Heads of State and Government of the AU in Addis Ababa, Ethiopia, on July 4.
In the letter, he said, "While thanking you for the kind words and for the nomination, I wish to express my readiness to accept this new important role and to reiterate my commitment to contribute towards our collective efforts to strengthen good governance and development on the continent.
"I, therefore, look forward to working closely with you in the realisation of this objective"