Yes, the software is capable to open and convert from/to MP4 and AMV video formats. This is actually specified on the official website. Here's what it says about it:
Read many formats, including HD Video, Blu-ray, HD Video, DVD, AMV, GIF, MP4 for PSP, Apple’s iPod and Archos, and many more.
As you can see, the video formats you've mentioned are there. Use the link posted below to find more about it: http://www.performersoft.com/video-performer.php