Jang Song Thaek, a once powerful leader in North Korea, was executed last week and deemed a traitor "for all ages," the Korean Central News Agency reported.
Kerry said the execution is "an ominous sign of the instability and of the danger that does exist" in North Korea.
"It tells us a lot about ... how ruthless and reckless [Kim Jong Un] is. And it also tells us a lot about how insecure he is, to a certain degree. It tells a significant amount about the instability internally of the regime, with the numbers of executions, this is not the first execution. There have been a significant number of executions taken place over the last months which we're aware of. And most importantly, it underscores the importance for all of us of finding a way forward with North Korea in order to denuclearize the peninsula," Kerry said.
Meanwhile, Kim Kyoung-hui, Kim Jong Un's only aunt, and his wife Ri Sol-ju have not been seen since the execution of Jang, the Korean Herald reported.
Media reports have questioned whether the women would make public appearances on Tuesday when the country holds a memorial ceremony to mark the second anniversary of the death of former leader Kim Jong Il.
Kim Kyoung-hui has been not been seen in the North's state-run media since September, prompting rumors that she is in failing health. Kim has been known to suffer from depression and alcoholism. She received a divorce from Jang last Wednesday, the day before he was executed under the directive of Kim Jong Un, Japan's Asahi Shimbun reported Saturday.
Ri was last seen out and about in October at a musical performance by a visiting Russian group. Rumors have been raised about a possible inappropriate relationship between her and Jang while she was a member of the Unhasu Symphony Orchestra.
Nine members of a musical troupe were executed in August in the North for making pornography, which was allegedly to cover up other sexual rumors surrounding Ri, the Asahi Shimbun said in September.