JPG to GIF without 256-colors-only restrictions

What is the easiest way to convert a JPEG file into a GIF with the original color depth? By specification GIF isn't restricted to 256 colors because every frame can have its own local color table. However, every application I found creates only one frame, and so the resulting GIF has only 256 colors.

GIF images can only handle 256 colours, although if you convert a JPG image to PNG instead you can use the full depth of colours available...