PRETORIA, South Africa (CNN) -- South Africans gathered in song and prayer late Thursday outside the hospital where Nelson Mandela is being treated, singing "Viva Mandela!" after news the South African anti-apartheid icon's condition had improved.
Colorfully dressed women danced in front of the Pretoria hospital where candles burned and people are often seen praying together, the South African Press Association reported.
Hundreds of people from the African National Congress Youth League and Women's League sang struggle songs, danced, and marched up and down the street in front of the hospital, according to the state-run South African Broadcasting Corp.
"There is no other like him," they sang of Mandela, the SABC reported.
Zuma: Mandela's condition improves
Mandela's condition improved Wednesday night, President Jacob Zuma said Thursday, as the eyes of the nation remained fixed on his progress.
Zuma spoke after visiting Mandela in the hospital and said Mandela's medical team told him the former president "remains critical but is now stable."
"I canceled my visit to Mozambique today so that I can see him and confer with the doctors. He is much better today than he was when I saw him last night," Zuma said.
Mandela, 94, considered the founding father of South Africa's modern democracy, has been undergoing treatment at the Pretoria hospital since June 8 for a recurring lung infection. Mandela's oldest daughter said earlier that although her father is critically ill, he opens his eyes and responds to touch.
"I reiterate that Tata is very critical, that anything is imminent," Makaziwe Mandela told SABC. "But I want to emphasize again that it's only God who knows when the time to go is. And so we will wait."
"Tata" is the word for father in the language of Mandela's Xhosa tribe.
"He's ... still reactive to touch. We will live with that hope until the final end comes," she said.
The stream of family visits continued, with the former president's granddaughter Ndileka Mandela and grandson Mandla Mandela the latest to come to the hospital, the South African Press Association said.
Concerned about rumors
Another grandson, Nkosi Mandela, issued a statement criticizing what he called "hurtful" and "mischievous rumors" about his grandfather's condition.
"Our government has been keeping all of us informed in this regard, and there is no reason to doubt the accuracy of the information they provide to the public," he said.
"At the end of the day, my grandfather's fate, like that of everyone else, lies with God and our ancestors," he added. "However, many of us will continue to pray and hope for his recovery."
An official briefed on Mandela's condition said he was on life support late Wednesday. Government spokesman Mac Maharaj declined to comment on the report, citing doctor-patient confidentiality.
Zuma's statement also warned against a rash of misleading reports about Mandela's condition.
"The presidency is disturbed by the rumors that are being spread about former President Mandela's health. We appeal for respect for the privacy and dignity of the former president," it said.
The governing African National Congress also said it was "disturbed by consistent rumors being peddled in the media and elsewhere" about Mandela's health.
The ANC is organizing prayer sessions around the country "where all South Africans can come together, hold hands and pray for Madiba, his family and medical team," it said in a statement Thursday.
In South Africa, Mandela is most commonly referred to as Madiba, the name of the Thembu clan to which he belongs. Referring to him as Madiba is a sign of endearment and respect, according to the Nelson Mandela Foundation.
'We need you!'
As the nation remained on edge, South Africans found solace in candlelight vigils. Police barricaded the street leading to the hospital's main entrance as crowds posted messages and left tributes at the hospital wall.
"We need you!" one sign read. "We love you tata, get well soon!" said another.
Police also cordoned off the street outside Mandela's Johannesburg home Thursday, the South African Press Association reported.
About 30 journalists who were gathered outside were asked to move to the end of the street, but well-wishers were still being allowed to leave flowers and tributes by the house.
'A hero for the world'
Mandela became an international figure while enduring 27 years in prison for fighting apartheid, the country's system of racial segregation. He was elected the nation's first black president in 1994, four years after he was freed.
Even as he has faded from the spotlight, he remains popular and is considered a hero of democracy worldwide.
He turns 95 next month.
U.S. President Barack Obama, who is on a tour of the continent this week that includes South Africa, said his thoughts are with the nation's citizens.
"He is a personal hero, but I'm not unique in that regard," Obama told CNN Chief White House correspondent Jessica Yellin in Dakar, Senegal, the first stop of his African tour.
"I think he's a hero for the world, and if/when he passes, we know his legacy will linger on throughout the ages."
First lady Michelle Obama said Mandela "is very much in our thoughts and prayers right now." Speaking to middle-school students in Dakar, she urged the children to "honor his legacy by leaving a proud legacy of your own."
"If President Mandela could hold tight to his vision for his country's future during the 27 years he spent in prison, then surely you all can hold tight to your hopes for your own future," she said.
"If President Mandela could endure being confined to a tiny cell, being forced to perform back-breaking labor, being separated from the people he loved most in the world, then surely all of us, we can keep showing up and doing our best -- showing up for school each day, studying as hard as you possibly can."
Obama's schedule does not include a visit with the anti-apartheid icon.The president's trip to South Africa this weekend includes a stop on Robben Island, where Mandela spent a majority of his prison term.
After South Africa, Obama plans to head to Tanzania, his last stop before returning to Washington.