The patient was in contact with a man, who had attended the Tablighi Jamaat congregation at Nizamuddin in New Delhi, the minister said.
Both of them are from Dhubri, however, it is not yet confirmed whether the new case had attended the relied patient attended the Jamaat event.
Meanwhile, the condition of the 65-year old retired BSF personnel from Hailakandi district, is alarming and he has been shifted to the Silchar Medical College Hospital, Sarma said.
The patient's other "parameters are stable but his oxygen saturation is decreasing and has been shifted to ICU of SMCH for better monitoring", he said.
The patient was confirmed COVID-19 positive on Tuesday night and had attended the Tablighi Jamaat event, with a travel history to Saudi Arabia.
There was no new case reported in the state on Wednesday and 27 of the 29 confirmed cases are related to the Tablighi Jamaat congregation, the minister said.
Sarma on Thursday visited the people who were stuck along the Assam-West Bengal border at Sriramour as they were in transit the day lockdown was imposed.
"They have completed their 14-day quarantine and we have initiated the process to send them back home after check up. I visited and enquired about their health with my colleagues," the minister said.
All people who arrived here from coronavirus affected countries or other states should remain under strict home isolation for 28 days from the date of arrival in Assam, irrespective of whether they are symptomatic or asymptomatic.
Meanwhile, the first batch of doctors, nurses and health workers attending to COVID-19 patients and quarantined patients, who completed their first week of duties, have proceeded to the mandatory 14-days of quarantine to designated places, including a five-star hotel, whose expenses will be borne by the state government, the minister added. DG RG RHL