How to convert batch of rectangular images into square images without cropping?

Question

Given batch of vertical and horizontal rectangular images :

rect-h.png

rect-v.png

How to convert batch of vertical and horizontal rectangular images into square images ?

So to get same sizes, not-cutted, no disformed :

rect-h-sq.png

rect-v-sq.png

---

I currently use

mkdir -p ./temp ./png                                  # create folders to work on copies of data and store final png output
cp ./* ./temp                                          # copies to ./temp, so to word on copies 
for file in ./temp/*.png                               # loop on the [edited] copies in ./temp
do
  keyIn=$(basename "$file" .png)                       # name of the file minus .png
  keyOut=$(basename "$file" .png)-sq.png               # name of the file minus .png, plus .-red.png 
  convert -background none -density 1200 ./temp/$keyIn.png -resize 300x300\! ./png/$keyOut   
done

But it fails.

Note: Density is there because I often work with svg as well.

Answer 1

Padding works :

mkdir -p ./temp ./png                                  # create folders to work on copies of data and store final png output
cp ./* ./temp                                          # copies to ./temp, so to word on copies 
for file in ./temp/*.png                               # loop on the [edited] copies in ./temp
do
  keyIn=$(basename "$file" .png)                       # name of the file minus .png
  keyOut=$(basename "$file" .png)-sq.png               # name of the file minus .png, plus .-red.png 
  convert -background none -density 1200 ./temp/$keyIn.png \
     -thumbnail '300x300>' -background white \
     -gravity center -extent 300x300 -resize 300x300\! ./png/$keyOut   
done