George Charamba said Mugabe, 89, who has been on his annual vacation, is well, Nehanda Radio reported.
Mugabe was filmed at the State House Sunday during a memorial for his sister, Bridget Mugabe, who died earlier in the day. The president, who will be 90 next month, is seen slouched in the corner of a sofa beside his wife, Nehanda Radio reported.
There has been much speculation about Mugabe's health. Last month, activist Baba Jukwa said on Facebook the president's health had deteriorated and he had collapsed.
Vice President Joice Mujuru carries out the presidential duties when Mugabe is on leave.
Bridget Mugabe, 79, died after almost four years in a coma. She had collapsed during a burial service for another sister in 2010 and was admitted at Parirenyatwa Hospital.
A statement from Mugabe said his sister was a woman who was fearless and courageous.
In a 1986 interview with the Herald in Harare, Bridget Mugabe said she was arrested for her role in Zimbabwe's war of liberation during the 1960s. She told the newspaper she refused to talk and was tortured for more than a month before she was released .