Israel's health ministry said Saturday four people had tested positive for the novel coronavirus strain first detected in South Africa, with the new British variant already recorded.
The cases were discovered after testing of travellers arriving from South Africa.
The two new strains are more infectious than previous variants of the virus.
Amid surging cases, Israel last month reimposed a national lockdown. On Friday it tightened restrictions further as the daily caseload remained high.
Israel has launched a nationwide vaccination programme and more than 70 percent of Israelis over the age of 60 have received a first dose, with 1.7 million jabs administered, according to the health ministry.
Prime Minister Benjamin Netanyahu, who was given his second jab on Saturday, said in a brief statement on Israeli television that all Israelis could be vaccinated within two months and "no later than the end of March".
Netanyahu announced Thursday that he had signed a deal for enough doses of the Pfizer-BioNTech vaccine for all Israelis over 16 to be innoculated.
Israel, with a population of nine million, has recorded over 3,600 deaths from the Covid-19 illness.