Godzilla came to America and was battled by SHIELD and the creatures of the evil Doctor Demonicus. He was eventually captured by Demonicus and mutated into an aquatic creature that he could control, battling Iron Man before breaking free. He appeared once more, attacking the production of Devil Dinosaur: The Movie, leaving after destroying their Devil Dinosaur robot.
This Godzilla was definitely intended to be the same as the Showa version. In his appearances after being captured by Demonicus, he was not specifically called Godzilla- however, it was definitely him.
A version of this Godzilla also exist in the Marvel (U.S.) Transformers universe. He was mentioned by Nick Fury in Transformers #3.