Of these six fresh infections, two were reported from Buxar district and four from Nalanda district.
Two members of a family, a 30-year-old man and a 28-year-old woman, from Buxar tested positive for COVID-19, said Principal Secretary (Health) Sanjay Kumar.
"Both persons (who are members) of a family from Buxar came in touch with a COVID-19 positive person who had travelled to Asansol," he said.
Buxar District Magistrate (DM) Aman Samir said the man and the woman are family members of two men who had tested positive for coronavirus on April 16. All of them live together.
Earlier, the DM had said that the two men, aged 35 and 67, had returned home on March 30 after taking part in a Tablighi Jamaat congregation in Asansol, West Bengal. They are believed to have picked up the infection from infected delegates at the congregation.
According to sources, the family hails from Naya Bhojpur village of Buxar.
Four other people, aged 12, 18, 22 and 55, tested positive for coronavirus in Nalanda's Biharsharif on Sunday, principal secretary Kumar said.
The 55-year-old man had come in "close contact with COVID-19 positive man who had returned from Dubai," he said.
So far, COVID-19 has claimed two lives in Bihar, one each in Munger and Vaishali districts.
Of the state's total 92 cases, Siwan district has reported the highest number of 29 cases, followed by Munger (17); Nalanda (11); Begusarai (9); Patna (7); Gaya (5); Buxar (4); Gopalganj and Nawada (three each); Lakhisarai, Saran, Bhagalpur and Vaishali (one each), a state government bulletin said.
Of the state's 38 districts, only 13 have reported COVID-19 cases so far.
According to the state health department, 42 COVID-19 patients have recovered till date and two have died.
The number of active cases in Bihar, including those reported on Sunday, stands at 48, it said.
A total of 10,130 samples have been tested in the state till date. AR CORR RG DIVDIV