Building docker image in azure

I need to build docker image (linux) in Azure. Right now I do this with VM running linux with docker installed. It all works, but it is hard for me to maintain this VM.

What I really want is to create docker image, which I will deploy and run in Azure, and this image will build other docker images.

My current understanding, that docker itself does not support this (except with privileged mode, which is not supported in Azure, or I do not know how to set in Azure). On the other hand I see there are some other products, such kaniko which possibly can do what I described.

My question is what is best (reliable, compatible) method to build docker image inside docker running in Azure cloud unprivileged?

Thank you very much in advance,