An assistant working for Oli also tested positive, they added.
Oli has previously tested negative, but had yet to take a test after his associates tested positive, press adviser Surya Thapa said.
"The prime minister has been exercising extreme caution while meeting with people," Thapa told Reuters.
Oli's personal physician had earlier tested positive and is isolating herself, Thapa said, adding that more than two dozen security personnel at Oli's official residence have also tested positive.
Nepal's Covid-19 cases rose by 2,120 to 84,570 on Saturday, the country's health ministry said.
Neighbouring India's coronavirus death toll passed 100,000 on Saturday, making it the third country to reach that milestone, after the United States and Brazil, and its epidemic shows no sign of abating.
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