Speculation over Nelson Mandela's health escalated last night as family members and senior political figures were seen visiting the frail 92-year-old in hospital. They included his ex-wife, Winnie Madikizela-Mandela, who reportedly left the hospital in tears.

Millions of South Africans were anxiously awaiting news of the former president's condition, but little news was forthcoming from the Milpark hospital in Johannesburg, where he was spending a second night.

The president's office said there is "no need to panic", South Africa's eNews reported, adding that Mandela is undergoing specialist tests necessary to give him optimal care.

Mandela is suffering an ailment common to people his age, the presidency was quoted as saying, but is in "high spirits" after being visited by family and friends.

Kgalema Motlanthe, the deputy president, told South Africa's SABC network: "I want to say to you, he's alive and kicking. He hasn't passed on." He added: "As you all know former president Nelson Mandela was admitted for a routine check yesterday in hospital. That has set the rumour mill into overdrive. Because of this overdrive people have been receiving SMSes indicating that he has passed on."

Zondwa Mandela, his grandson, told the Bloomberg agency: "He is in good health and good spirits."

Reuters last night reported that Mandela was recovering from a collapsed lung, and could be released as early as Friday, according to a source close to Mandela. However, the Nelson Mandela Foundation, which said on Wednesdaythat Mandela was "undergoing routine tests" and was "in good spirits", declined to clarify the situation.

Anguished rumours abounded on Twitter and elsewhere as South Africa contemplated the loss of its moral lodestar, an event that will be a national trauma.

The president's office appealed for calm. "We urge the media to afford him the dignity and respect that he is entitled to as the country's founding democratic president, as a national hero and as a citizen of the republic," it said. "President Mandela is comfortable and is well looked after by a good team of medical specialists."

It added that President Jacob Zuma, attending the World Economic Forum in Davos, Switzerland, was being "kept abreast of developments" – implying the tests are no longer routine.

A close of friend of Mandela, who did not wish to be named, said there was "no cause for alarm". But some regarded the steady stream of visitors to the hospital as an ominous sign.

Mandela undergoes regular hospital checkups, but his latest visit has stretched into an unusually long stay.South Africa's Star newspaper reported that he had been airlifted from Cape Town to Milpark hospital by military aircraft after developing a persistent cough. The hospital did not comment.

Police were called in to control traffic at the hospital as scores of journalists, photographers and TV crews converged on the building.

Children at neighbouring McAuley House primary school created "Get well soon" banners and shouted from classroom windows: "Get well Madiba [his clan name]. We love you Madiba."

Meanwhile, police cordoned off the entrance to Mandela's house in the Johannesburg suburb of Houghton. Police said this was as a precaution in case people wanted to pay homage.

Leading South Africans offered their best wishes. Archbishop emeritus Desmond Tutu said he saw Mandela last week and remarked that for a 92-year-old he was "amazing". Tutu said to journalists in Bloemfontein: "What more do we want from him? We want him to remain forever, but, you know … anything can happen."

Meanwhile the White House said President Barack Obama and first lady Michelle Obama's thoughts and prayers are with Mandela.

Mandela, the hero of South Africa's liberation struggle who spent 27 years behind bars, had done a fantastic job, and the country should thank God for him, Tutu added.

The governing African National Congress denied that there was serious grounds for concern.

"He is a 92-year-old and will have ailments associated with his age, and the fact that he stayed the night should not suggest the worst," a spokesman, Jackson Mthembu, said.

"We urge people not to make unfounded statements. Let's remain calm and not press panic buttons because there is no reason to do so." a spokesman said.

He added: "We appeal, particularly to the media fraternity, to refrain from making unfounded and unwarranted speculation in relation to Madiba's health."

Mandela was treated for tuberculosis during the 1980s, and later had an operation to repair damage to his eyes. In 2001 he had treatment for prostate cancer.

He retired from public life in June 2004 ahead of his 86th birthday, telling his adoring compatriots: "Don't call me. I'll call you."

He has not been seen in public since the final of the football World Cup in July last year. Speculation about his health has frequently flared up.

Earlier this month the ANC said it wanted Twitter to take action after a hoax report of Mandela's death was widely distributed on the microblogging site.