Of the 24, 11 are from Goalpara, three each from Nalbari and Tinsukia, two from Dibrugarh and one each from Kamrup, Nagaon, Karbi Anglong and Dhubri.
The details of one case were yet to be determined, the minister said.
All 24 cases were detected late on Thursday, raising the day's total to 97.
Sixteen patients were discharged from two hospitals following their recovery -- 15 from the Mahendra Mohan Choudhury Hospital and one from the Silchar Medical College Hospital. The number of recoveries in the state rose to 103.
Assam currently has 770 active patients. Four have succumbed to the viral disease and three have migrated.
The state had been witnessing a surge in COVID-19 cases, with 813 people testing positive for the disease since travel restrictions were lifted on May 4.
Prior to that, it had only 42 coronavirus cases.
As many as 493 cases have been detected so far this week. The biggest single-day spike was recorded on Monday with 156 cases.
Sarma said that the latest cases could be mostly attributed to those that have recently returned to the state.
The government has mandated that all coming from outside will have to undergo institutional quarantine. No home quarantine will be allowed for the first seven days, till the test results arrive.
Altogether 86,340 samples have been examined so far, 77,614 of which tested negative for the disease and the results of the rest are awaited, according to the Health and Family Welfare Department.
As of date, there are 46 containment zones in Assam.
Meanwhile, flight operations to and from Dibrugarh and Tezpur airports began from Thursday, with each operating single flights during the day, an airport spokesperson said.
Passenger flight services from the Lokopriyo Gopinath Bordoloi International Airport had resumed on Monday. DG RMS DV DV