Harare, Zimbabwe (CNN) On a day Zimbabwe's President Robert Mugabe appeared in public for the first time since his nation plunged into political crisis, his ruling party is reportedly calling for him to step down.

"ZANU-PF provincial structures in all the country's 10 provinces met today and called for the resignation of their First Secretary, President Robert Mugabe. They also called for the resignation of women's league Secretary and First Lady Dr Grace Mugabe from the party," State newspaper The Herald reported Friday

Mugabe emerged from house arrest to attend a university graduation ceremony in the capital, Harare, in a staged public appearance that belied the reality that he is no longer in control of the country he has ruled for 37 years.

The veteran leader arrived at Zimbabwe Open University in a blue-and-yellow gown, accompanied by his security detail, in his first public appearance since being detained in Wednesday's army takeover.

There was no sign of Mugabe's wife, whom the leader was trying to promote as the next president, triggering the political upheaval.

Zimbabwe's President Robert Mugabe, right, arrives at the Zimbabwe Open University in Harare.

The developments were the latest in an increasingly bizarre set of events that has eschewed the traditional playbook for military takeovers.

Mugabe's appearance was apparently designed to convey a business-as-usual atmosphere -- the generals pulling the strings in Harare are desperate not to give the impression they are orchestrating an unconstitutional coup.

But behind the scenes, efforts to push Mugabe aside appeared to be foundering. Mugabe was reported to be resisting a plan to oust him, and the generals were said to be frustrated by his refusal to go quietly.

Latest developments

Mugabe resisting deal: The President has pushed back on a deal to replace him with an interim leader, a source told CNN.

Military sets deadline: Frustrated with Mugabe's resistance, the commander of the defense forces said the President had until Friday to change his stance, "or we do it the hard way," a source said.

Tillerson weighs in: US Secretary of State Rex Tillerson described the situation as an "opportunity" and called for democratic elections.

An anti-Mugabe march: Zimbabwe's military says it supports a peaceful and orderly march against Mugabe, scheduled to take place in Harare's Zimbabwe Grounds in Highfield on Saturday.

Transition talks

As Mugabe arrived at the graduation ceremony Friday morning, Zimbabwe's political limbo was entering its third day and clandestine efforts to prise Mugabe from power appeared to have reached an impasse.

According to a government source with direct knowledge of the talks, Mugabe had pushed back on a deal to replace him with an interim leader, arguing there would be a constitutional crisis if he left before his term expired.

Mugabe was photographed Thursday in talks with army chief, Gen. Constantino Chiwenga, and other officials at the official State House.

The source told CNN that the photos were "merely a formality" and a deal that had already been done. Part of the deal was that an acting president would be named, as required by the constitution when there is no vice president, the source said.

Mugabe in talks about his future, in this image tweeted by the editor of Zimbabwe's Herald.

But a day later, it was clear Mugabe was digging his heels in.

Frustrated with the lack of progress, the commander of the defense forces, Chiwenga set a deadline of Friday for Mugabe to agree to a deal, "or we do it the hard way," the source said.

Meanwhile, at Zimbabwe Open University, on the outskirts of the capital, Mugabe conferred degrees on students as if nothing was untoward.

But if he thought that attending the event would make it look as if he was still in charge, the tactic backfired. The 93-year-old said little and drifted in and out of sleep on stage.

The political firestorm was ignited by Mugabe's dismissal of his powerful vice president, Emmerson Mnangagwa.

Mnangagwa has strong connections and the support of the military, and under the deal apparently on the table with Mugabe, he would run for the leadership of Mugabe's ZANU-PF at a congress in December, allowing him then to contest next year's presidential elections.

CNN has learned that Mnangagwa had been instrumental for some time in plans to seize control from Mugabe, who had been maneuvering to anoint his wife Grace as his successor.

"This takeover was planned a long time ago by Emmerson Mnangagwa and secret discussions did take place with opposition about a succession plan including forcing out Mugabe," a senior opposition leader with direct knowledge of the talks told CNN.

Mnangagwa's whereabouts were unknown, but he was widely reported to be guiding events. The influential Zimbabwe National Liberation War Veterans Association, which has thrown its support behind Mnangagwa, is planning a huge show of strength in Harare Saturday.

"We will settle the scores tomorrow," Chris Mutsvangwa, head of the association, told reporters on Friday. "There is no going back about Mugabe, he must leave," he said.

Foreign powers have called on the military to show restraint in the upheaval, but have largely supported its actions so far.

Tillerson hosted a ministerial meeting on African trade, security and governance on Friday, where he described the situation in Zimbabwe as an opportunity for the country.

"Zimbabwe has an opportunity to set itself on a new path, one that must include democratic elections and respect for human rights," he said at the event in Washington, calling for a quick return to civilian rule.

New normal

Not too long ago, Mugabe's presidential guard would have died defending their leader. But this week, CNN saw several armored personnel carriers (APCs) stationed outside their headquarters in Harare -- a clear sign that the military is hemming them in.

Tanks were still positioned in downtown Harare and no police were to be seen , though the city was "calm" with shops and businesses open, residents reported.

The military has denied that the events of the week amount to a coup, but residents were still unclear as to what type of rule they would be living under.

"We don't know what is happening," one man told CNN. "What we know is that the soldiers are in control."

Zimbabweans are cautious, but hopeful that, after almost four decades of often brutal rule, Mugabe -- who has governed for longer than many of his countrymen have been alive -- could be coming to an end.

Another Zimbabwean CNN spoke to said that Mugabe should leave office, and end the economic ruination of the African country once known as Africa's breadbasket.

"We need a new president," he said, peering through his car's window. "We need bread and butter."