Welcome to the forum.
One more question: which H.264 CODEC do you have installed?
Some users have had issues with the Apple H.264, though that is usually upon Export, and not Import. In many of those cases, the users have had much better results with the Lead, or MainConcept H.264 CODEC's.
Also, when you have Imported the H.264 files, if you drag one to the New Icon at the bottom of the Project Panel, to create a new, matching Sequence. how do the files play in that? (So I that does make two questions... )
Premiere Pro was designed to work with standard camera formats. Sometimes it works fine with non-standard formats, sometimes it doesn't.
As there are no cameras that record MP4 into an AVI file, you are using a non-standard format. Since it doesn't work, the solution here is not to use those files.
Read the 2nd post for NEW ITEM pointer http://forums.adobe.com/thread/770072?tstart=0 and follow the instructions, to let PPro analyze the file for you
This is not going to help in the OP's circumstance; if the video doesn't play in Premiere, it's not going to magically start playing once dropped on the New Item button. That sets up a sequence with parameters that match the footage (is that what you mean by letting "PPro analyze the file?"), but Premiere is pretty black-or-white when it comes to format/codec support--it plays everywhere or it doesn't play at all.
If that were not true, DV footage would have to be edited only in a DV sequence, and AVCHD only in an AVCHD sequence. Of couse, that's not the case--sequences are format-agnostic.