Is it possible to make a rifle w/the rugged reliability of an AK but the accuracy of the M16 variants?

Several good answers in response to the post. Good thing you didn't add low COST to the criteria. Now THAT would have been nearly impossible.

HK-91, or for something made here in the USA the PTR-91. Plus you get a boost in caliber: 308 Win.

Basically any piston AR15.