PRETORIA, South Africa (CNN) -- The condition of South African anti-apartheid icon Nelson Mandela has improved overnight, President Jacob Zuma said Thursday, as the eyes of the nation remained fixed on his progress.

Zuma, whose statement came after he visited Mandela in a hospital in Pretoria, 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.

Earlier, Mandela's oldest daughter said 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 state-run South African Broadcasting Corp. "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 Xhosa word for father.

"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.

Zuma's statement also warned against the 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 state of health.

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.

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!'

Shortly after visiting Mandela on Wednesday night, Zuma canceled his planned trip to Mozambique, where he was due to attend a summit on investment Thursday.

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 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 an 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."

Obama's visit to South Africa on Saturday will include a visit to Robben Island, where Mandela spent a majority of his prison term. The White House schedule does not include a visit with the anti-apartheid icon.

After South Africa, Obama heads to Tanzania, his last stop before he heads back to Washington.

CNN's Faith Karimi wrote and contributed from Atlanta, and Robyn Curnow from Pretoria, while Laura Smith-Spark wrote in London. CNN's Brent Swails, Josh Levs, Samira Said and Pierre Meilhan contributed to this report.