Forty-seven people were still unaccounted for, including the 11 with whom contact had been established.
“We are in contact with 11 people” trapped under rubble, Colin Deiner, head of rescue operations, told a news conference in Cape Town.
Life had been detected under three areas of the site.
“They’ve been down there for more than 24 hours now, that’s a long time” provincial premier Alan Winde said at the same news conference.
Recalling that the international standard for a rescue operation is three days, he said the second day would be “critical”.
Authorities also added that they had advised the 11 to switch their phones on and off to preserve battery power.
The main focus is to get everyone out, Deiner said. “Once we have got all the people that we know about out, we are going to start a process called delayering,” he added.
“We would then start lifting the different floors off each other,” he said, adding it would be “tricky” to remove the concrete trapping the building workers.
A construction crew of 75 people was on site at the time of the collapse at around 2:00pm local time on Monday, authorities said.
Three rescue teams were working on three different areas of the collapsed building, which included an underground car park.
The reasons for the collapse were still unknown.
The construction plans for a 42-unit block of flats had been approved by the city in July.
President Cyril Ramaphosa offered his “deep condolences to the relatives and friends” and said his thoughts were with the families of the dead and missing.
He called for an investigation, saying it must “bring closure to the community and prevent a repeat of this disaster”.
George, which has a population of about 160,000, is a picturesque coastal city located on the tourist trail along South Africa’s southern coastline.
Photos shared by the city council showed a flattened construction site with emergency services on the ground.
The broken roof of the building was still clearly visible atop the pile of rubble.
Rescue operations had continued throughout Monday night, with floodlights illuminating the cordoned off site.
A coordination post was set up to run the operations, which involve numerous emergency services and over 200 personnel.
More diggers and sniffer dogs were dispatched from Cape Town, emergency services said.
Officials said relatives of those trapped had been asked to gather at the city hall near the construction site, where they would be taken care of.
Religious leaders and social workers were present to assist and comfort families, authorities said.
No stone will be left unturned in making sure that we get to what caused this accident
“Our thoughts are with the families and all those affected, who continue to wait for word of their loved ones,” Mayor Leon van Wyk said.
But officials urged onlookers and members of the public to stay away from the “dangerous” site.
They also urged South Africans to refrain from posting fake news about the disaster.
George is run by the Democratic Alliance, the leading opposition party, which also controls the Western Cape province.
“No stone will be left unturned in making sure that we get to what caused this accident,” Winde vowed.