Zimbabwean President Robert Mugabe has celebrated his 93rd birthday, defying calls to resign after nearly four decades in power.

Thousands of government supporters, some wearing clothing adorned with Mugabe's image, converged in Matabeleland for a birthday bash and show of strength for the ruling ZANU-PF party.

Mugabe, a former rebel leader who took power after independence from white minority rule in 1980, declared a few days ago that most Zimbabweans think nobody can replace him.

The longevity of the world's oldest head of state is a source of heartache for Zimbabwe's splintered opposition and uncertainty for investors, leaving the economically struggling country in limbo.

Mugabe on Saturday wore dark glasses and a multi-coloured jacket bearing an image of himself in younger days, sitting impassively as speakers praised his leadership.

Delegates from ruling parties in Botswana, Namibia, Angola and Zambia greeted him and the Chinese ambassador read a congratulatory message from President Xi Jinping.

At one point Mugabe raised his fist in salute.

Zimbabwe's challenges include a strike by doctors over working conditions that has forced army and police doctors to deploy in public hospitals. Conditions at hospitals were already deteriorating because of poor staffing and low supplies of medicine.

The government has endured other crises, rejecting decades of opposition and Western allegations about human rights violations, voting irregularities and economic mismanagement.

Mugabe, who turned 93 on Tuesday, has been serenaded at a palace cake-cutting by singers who wished him "many more" birthdays.

Air Zimbabwe, the cash-strapped national carrier, and other entities took out birthday notices in pro-government media. Dancers and musicians performed ahead of Saturday's party at a school in Matopo Hills, on the outskirts of Bulawayo city with caves and rock art dating back thousands of years.