Griffiths arrived on Saturday in Turkey's southern city of Kahramanmaras, the epicentre of the first 7.8-magnitude tremor that upturned millions of lives in the pre-dawn hours of Monday, Al-Monitor reported.
He said of the death toll in an interview with Sky News on Saturday: "I think it is difficult to estimate precisely as we need to get under the rubble but I'm sure it will double or more."
"We haven't really begun to count the number of dead," he said.
Officials and medics said 24,617 people were killed in Turkey and 3,574 in Syria. The confirmed total now stands at 28,191.
Tens of thousands of rescue workers are scouring flattened neighbourhoods despite freezing weather that has deepened the misery of millions now in desperate need of aid.
The United Nations has warned that at least 870,000 people urgently need hot meals across Turkey and Syria. Up to 5.3 million people may have been made homeless in Syria alone.
Almost 26 million people have been affected by the earthquake, the World Health Organization (WHO) said as it launched a flash appeal on Saturday for $42.8 million to cope with immediate health needs.
Turkey's disaster agency said more than 32,000 people from Turkish organisations are working on search-and-rescue efforts. There are also 8,294 international rescuers.
"Soon, the search and rescue people will make way for the humanitarian agencies whose job it is to look after the extraordinary numbers of those affected for the next months," Griffiths said in a video posted to Twitter.
Reporter's code: 50101