Of the fresh cases, one is in Jammu and the rest in Kashmir, they added.
"Twenty-three new cases have been reported from Jammu and Kashmir in the last 24 hours," an official said.
With Reasi district in Jammu division reporting its first COVID-19 case, the virus has now spread to 18 of the 20 districts in the Union territory.
Of the total number of cases reported so far, 488 are from Kashmir and 58 from Jammu. Seven people have died and 164 patients have recovered. The number of active cases stands at 375.
Nearly 67,000 people have been put under surveillance in the UT, including those who are either in government-established quarantine facilities or in home-isolation.
Out of them, 49,338 people have completed their surveillance period, the officials added. MIJ IJT