Which filling and adhesive material is suitable for interior window sills made of stone/marble?

Hello everyone,

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see attachment. Our new windows partly have two window sills at the bottom, each about 3 cm. With which material would you fill the area below? What would be suitable here?

Has no one had a tip or similar filler actions?

So I had an average of 4.5 cm. I filled that once with a few blobs of tile adhesive that I still had left. Just that thick and then the windowsill on top. The rest with foam, then plastered.
For the remaining windows the same with Perlisan insulating plaster, but because it didn’t adhere that well I then distributed plastic mounting blocks. For one windowsill I also had nearly 6 cm and there I applied it layer by layer.
So far everything seems to be holding...

Super thanks. A few spots and remaining foam sounds interesting. I might have thought too complicated and had considered encasing it a bit and pouring something in and only then gluing the rest

Yes, I had that at the beginning too. I would like to point out that you have much more elevation difference. That definitely makes a difference. How much contact area does the bench have?

If you use marble or other natural stone, please do not use regular tile adhesive, but natural stone adhesive. The regular one can sometimes cause unsightly stains on the surface. I also adjusted the height using wood and plastic wedges and glue.