About 783,000 new cases are reported on average each day globally, almost half in India, where a virus variant, B.1.617, has been spreading.
Home kits and mobile testing units have already been rolled out in Bolton, which has one of the highest rates of B.1.617.2 in England.
The WHO has said the predominant lineage of B.1.617 was first identified in India last December, although an earlier version was spotted in October 2020.
The experts, however, said the new variants detected in South Africa were not driving the surge.
The B.1.617 variant is the fourth variant to be designated as being of global concern and requiring heightened tracking and analysis.
Saskia Popescu, an infectious-disease expert who is an assistant professor at George Mason University, said that Americans should not be lulled into thinking the virus is defeated, because "we have to see the crisis in India as a wake-up call for global vaccine equity and that COVID-19 isn't gone anywhere until it's gone everywhere".
On Saturday, the institute confirmed that the COVID-19 variant first detected in India, B.1.617.2 arrived in the country, with four confirmed cases.
"Globally, we are still in a perilous situation", Tedros said.
Monday's 366,161 new infections and 3,754 deaths reported by India's health ministry were off a little from recent peaks, taking India's tally to 22.66 million with 246,116 deaths.
They are the first confirmed cases of the variant in the region.
Mkhize said of the 11 cases of the B.1.1.7 variant first detected in the United Kingdom, eight were detected in the Western Cape, with two having a history of travel from Bahrain, one was detected in KwaZulu-Natal and two in Gauteng.
The government itself has not carried out whole-genome sequencing of the virus to study the variant circulating in the country of late despite the rapid spread of the infection for the last several weeks.
"That's going to be a problem for the whole world".
The Department of Health said COVID-19 travel restrictions needed to be balanced with the need to grow the economy.
Scientists believe it is at least as infectious as the variant originally detected in Kent previous year, which went on to become the dominant version of coronavirus in the United Kingdom, though chief medical adviser Chris Whitty said on Monday that it appears less likely to escape the body's immune response than other variants.
Dr Van Kerkhove said much more information was needed about the variant, while Soumya Swaminathan, WHO chief scientist, said further studies were under way in India to examine the variant's transmissibility, the severity of disease it causes and the response of antibodies in people who have been vaccinated.