In South Africa, which was the first country to report the highly mutated variant, 8,561 new coronavirus infections were registered in the latest daily figures - around double the 4,400 cases confirmed the day before.
Although only a limited number of positive tests have been analysed, the country's National Institute for Communicable Diseases (NICD) has said more than 70% of all the virus genomes it sequenced last month have been of the new variant.
"It looks like there is a predominance of Omicron throughout the country," Professor Anne von Gottberg, from the NCID, told a World Health Organization news briefing on Thursday.
"The numbers are increasing very, very quickly. We are up to 8,000 (daily cases), I think we'll be up to 10,000 today."
Designated a "variant of concern", Omicron has now been detected in at least 24 countries around the world, according to the WHO, with at least 32 cases identified in the UK so far.
On Thursday, India confirmed its first cases of the Omicron coronavirus variant in two people who travelled abroad.
The country's health ministry said the cases include two men in southern Karnataka state who came from overseas - without specifying which country.
Saudi Arabia and the UAE are also among the latest countries to have confirmed their first cases of Omicron. As the world rushes to halt its spread by imposing travel restrictions from many southern African countries, new infections are expected to increase in what is now the beginning of the fourth wave in South Africa.
Listen to our coronavirus podcast for the latest analysis
On Wednesday, the NCID said the majority of new cases were from the provinces of Gauteng (72%), followed by Western Cape and KwaZulu-Natal.
Dr Abdou Salam Gueye, the Regional Emergency Director for the WHO Africa region, told the news briefing that Ghana and Nigeria have become the latest African countries to detect the Omicron variant.
"Thankfully, the speed and transparency by Botswana and South Africa in detecting and alerting the world to the new variant has given us an early start in mounting an effective response," he said.
"We must seize this window of opportunity, act swiftly to ramp up measures to track, detect and control the spread of the Omicron variant."