Nirat said he will consult with local medical staff before deciding whether to relax some rules governing people and trade.
The northeastern province will lift more restrictions if it reaches 21 days without any confirmed new cases.
Earlier the province enjoyed a run of eight consecutive days without fresh infections, before a case of Covid-29 emerged on April 3.
That brought the total confirmed cases in Udon Thani to eight. Six have recovered and returned home while two remain in hospital.
Bangkok temple offering Songkran relief amid contagion
The popular Wat Samian Nari in Bangkok’s Chatuchak district has taken measures to cut the risk of Covid-19 infection during this week’s Songkran festival.
The temple has opened its doors to worshippers who wish to make merit, but will not be holding any religious activities.
Visitors are also having their temperatures checked at the screening point as they enter, where they will also find bottles of the ubiquitous alcohol sanitizer to cleanse their hands.
For those who want to offer alms, the temple has set up a clear plastic partition to separate monks and worshippers, as well as arranging chairs to maintain social distancing.
In addition, the temple has opened a relief centre to distribute rice, dry foods, and essential goods to people suffering impacts from the Covid-19 outbreak.
Temple authorities said they have also prepared safe cremation arrangements for anyone who dies after contracting Covid-19.