One GIF feature that PNG does not try to reproduce is multiple-image support, especially animations; PNG was and is intended to be a single-image format only.
Source: www.libpng.org
Edit: An animated PNG is therefore a non-standard extension to PNG, and as such cannot be guaranteed to be supported by any program, now or in the future.
There is a PNG-based animation standard called MNG, and that's the format that is being pushed.