The premier added that the position would not be left vacant or projects ignored, adding that the deputy minister can fill the post and he himself, as economic chief, could keep an eye on things.
The premier also said he would promote a suitable person to take over the job.
Prayut also confirmed that Predee had resigned due to genuine health problems.
The new finance minister tendered his resignation on Tuesday, and it was announced on the Royal Gazette the same day. His resignation goes into effect on Wednesday.
In an exclusive interview with Bangkokbiznews under the Nation Group, Predee denied having any conflicts with Deputy Finance Minister Santi Promphat, saying they could work together effectively despite having different approaches and views about management.
Predee is the sixth finance minister to quit soon after taking the position. Pote Sarasin spent just four days as finance minister after elections in 1957.