On having talked at length with Gulliver over the period of time that Gulliver spent with the Brobdingnagians, the King comes to the final conclusion that Gulliver and the Europeans are "the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth." This is based on Gulliver's multiple stories about the way they live, customs, manners, and also his demonstration of gunpowder which shocked and dismayed the audience.
I assume you are referring to Part II of Gullier's Travel's since that is the first mention of a king; the land of Lilliput in Part I is ruled by an emperor. The king thinks Gulliver, at first glance, is a splacknuck - described in chapter 2 as "an animal in that country very finely shaped, about six foot long". Then, when the king saw Gulliver stand upright and heard him speak, considered Gulliver to be a clockwork toy of great design. Gulliver, very adept at languages and having learned a little of the Brobdingnagian language at this point, communicated to the king that he was not a toy. The king then had three scholars study Gulliver. They finally concluded that he was a "lusus naturae", or, "a freak of nature".