As many as 111 new cases were detected late tonight, adding to the 34 during the day, the Minister said.
Two persons have died due to the disease this week, taking the toll to six in the state.
A 67-year-old cancer patient, who had recently returned from Mumbai, died at the Tezpur Medical College Hospital on Wednesday and another person with a travel history to Chennai passed away on Monday.
Meanwhile, 183 patients were discharged from various civil, district and model hospitals in the state, taking the total number of recovered patients to 1,432 on Thursday with the highest number of 313 released on Tuesday.
Of the total 3,430 cases, 1,989 persons are active, 1,432 have recovered, six have died and three migrated out of the state, the Minister said.
Assam has witnessed a surge in COVID-19 positive cases since inter-state movement of people began, with more than 3,000 cases added since May 4 and the figures increased rapidly since the last week of May.
On May 4, there were only 42 reported cases in the state and it crossed the 100-mark on May 17 reaching the 500-mark on May 25.
The 1,000-mark was crossed on May 29, the 2000-mark on June 4 and more than one 1,000 cases were added in five days to cross the 3000-mark on June 9.
Assam has 94 containment zones currently with Cachar having the highest of 33 zones, followed by Kamrup (Metro) with 27, Golaghat with six, Dhubri and Darrang with five each, Goalpara, Kamrup (Rural) and Majuli with three each, Karbi Anglong with two, Charaideo, Karimganj, Kokrajhar, Hojai, Nagaon, Baksa and Bongaigaon with one each.
The Minister visited the Lokpriyo Gopinath Bordoloi International Airport here on Thursday to inspect screening facilities for passengers and urged airport officials to take full protection and care.
He also reviewed containment measures and other facilities to ensure best preparedness to deal with COVID-19 in the state.
The Assam government's aim was now for reduced institutional-quarantine, increased home-quarantine and further increase testing during June.
Assam has so far tested 1,81,108 samples till date and out of these 3,430 have tested positive, 1,71,070 have tested negative and the remaining results are awaited, the state Health and Family Welfare Department said in its daily bulletin.
Meanwhile, in view of the current COVID-19 outbreak and to check its spread in the community, the health department will conduct the second round of the Assam Community Surveillance Programme (ACSP), covering all villages and wards of the state this month.
The first round of the community surveillance was held last month and 29,771 villages were covered with only 26,000 people showing signs of fever but not a single COVID-19 positive case was reported from the community, the Minister had said. DG TIR TIR