Zimbabwean President Robert Mugabe has made his first public appearance since the military put him under house arrest, attending a graduation ceremony on the outskirts of Harare.

His appearance came as the military announced “significant progress” on talks for his departure and arrested some of his allies.

Branches of the ruling party have also begun to pass no-confidence votes in the world’s oldest head of state.

Mugabe attended the Zimbabwe Open University graduation event, to polite applause, amid an extraordinary series of negotiations with regional leaders over his departure after 37 years in power.

Zimbabwe’s military is taking pains to show respect for the 93-year-old by referring to him as the president and the commander-in-chief.

But some in the ruling Zanu-PF party signalled they were getting impatient with Mugabe, with party branches passing no-confidence votes in the provinces of Mashonaland East and Manicaland.

Others among the country’s 10 provinces, including Midlands, Masvingo and Harare, were said to be following suit.

Parliament is expected to resume sitting on Tuesday. It is possible that Zanu-PF could use party procedures to impeach Mugabe with the support of opposition legislators.

Mugabe has asked for “a few more days, a few more months”, the chairman of the influential war veterans’ association in Zimbabwe told reporters.

Chris Mutsvangwa, an ally of the recently fired vice president Emmerson Mnangagwa who is expected to lead any new government, said that “between now and tomorrow” they will warn Mugabe that the game is over.

“If he doesn’t leave, we will settle the scores tomorrow.”

Mr Mutsvangwa also said three cabinet ministers have been arrested in the military’s efforts to pursue Mugabe allies.

Education minister Jonathan Moyo, local government minister Saviour Kasukuwere and finance minister Ignatious Chombo “are in jail” along with a number of others.

Mugabe did not make a speech at the ceremony, merely announcing its opening to applause after joining the crowd in the national anthem.

Arriving in suit and tie, he put on an academic gown and hat and walked slowly in a red-carpet procession to a podium as a marching band played.

The military statement reported by the state-run Herald newspaper and Zimbabwe Broadcasting Corporation said its leaders were “engaging with the Commander-in-Chief President Robert Mugabe on the way forward and will advise the nation of the outcome as soon as possible”.

“Significant progress has been made in their operation to weed out criminals around President Mugabe,” the statement said, adding that the military had arrested some while others remained at large.

They had been “committing crimes that were causing social and economic suffering in Zimbabwe”.

Ms Mugabe’s rapid political rise had alarmed many who feared she could succeed her husband after he fired his long-time deputy Mr Mnangagwa last week. That firing set off the military’s moves.

There was no sign of the first lady, Grace, at yesterday's graduation ceremony.

Army troops and armoured vehicles continue to patrol the capital Harare as Zimbabweans go about their daily business.

Residents said they had feared at first when the military moved in but praised the current calm.

Others told our sister newspaper, USA Today, that after years of famine, joblessness, corruption and human rights abuses, they hope the country's fortunes will change following Mugabe's departure.

Talent Zvinorwadza, who has been unemployed for years, hopes that his life will improve following the apparent ouster of the world's oldest leader after nearly four decades of rule in this southern African nation.

"I have a family to look after and I am excited by this development," Zvinorwadza, 35, an unskilled labourer. "I am looking forward to getting a job very soon."

"Mugabe and his wife must leave the country immediately," said Paida Murahwa, 28, a dressmaker. "Mugabe has violated the rights of many activists and has run down the economy."

Some remembered what Mugabe had done for the country, seizing power in 1980 from minority white rule of what had been known as Rhodesia. They believe the ageing leader should now be allowed to retire with dignity.

"Mugabe fought for our freedom and he should not be treated like this. He deserves an honourable exit," said Stephen Mukombwe, 39.

But university student Emily Phiri says his departure marks a new chapter for Zimbabwe.

"If he is really gone that is good for the country," said Ms Phiri, 19. "I think there will be lots of investment and jobs created. I look forward to getting a good job with a very good salary and I will buy nice things."