The 88-year-old was met by party leaders and military chiefs at Harare’s main airport, under usual protocol.
The party said reports that Mugabe was gravely ill were “a lot of hogwash” from hostile Western media groups.
Mugabe has made 10 trips to Singapore in the last 16 months, reportedly for medical treatment for prostate cancer.
Local newspaper the Zimbabwe Mali reported that the leader was on his “deathbed” but those close to Mugabe insisted that he was “energetic and alert” and spending Easter with his family.
The president has called for elections this year and has been nominated as his party’s only candidate for president.
Speculation on his health came after a popular Nigerian preacher predicted the deaths of elderly autocratic southern African rulers.
The death of Malawi’s 78-year-old president came soon after, on April 5.
Zimbabwe’s information minister Webster Shamu said the media had “spread rumours”.
He added: “”As you can see, he is fit as a fiddle. Why do we spread rumors? It’s all lies told by a press driving an imperialist agenda.”
The leader, who shares power in a coalition with rival Prime Minister Morgan Tsvangirai, is expected to chair a weekly cabinet meeting later today, which will be closed to the media.