Narada informed Kamsa that in his previous birth Kamsa was Kalanemi, a demon killed by Visnu

SB 10.1: The Advent of Lord Krsna: Introduction: Formerly an asura named Kālanemi had six sons, named Haṁsa, Suvikrama, Krātha, Damana, Ripurmardana and Krodhahantā. They were known as the ṣaḍ-garbhas, or six garbhas, and they were all equally powerful and expert in military affairs. These ṣaḍ-garbhas gave up the association of Hiraṇyakaśipu, their grandfather, and underwent great austerities to satisfy Lord Brahmā, who, upon being satisfied, agreed to give them whatever benediction they might desire. When asked by Lord Brahmā to state what they wanted, the ṣāḍ-garbhas replied, "Dear Lord Brahmā, if you want to give us a benediction, give us the blessing that we will not be killed by any demigod, mahā-roga, Yakṣa, Gandharva-pati, Siddha, Cāraṇa or human being, nor by great sages who are perfect in their penances and austerities." Brahmā understood their purpose and fulfilled their desire. But when Hiraṇyakaśipu came to know of these events, he was very angry at his grandsons. "You have given up my association and have gone to worship Lord Brahmā," he said, "and therefore I no longer have any affection for you. You have tried to save yourselves from the hands of the demigods, but I curse you in this way: Your father will take birth as Kaṁsa and kill all of you because you will take birth as sons of Devakī." Because of this curse, the grandsons of Hiraṇyakaśipu had to take birth from the womb of Devakī and be killed by Kaṁsa, although he was previously their father. This description is mentioned in the Hari-vaṁśa, Viṣṇu-parva, Second Chapter. According to the comments of the Vaiṣṇava-toṣaṇī, the son of Devakī known as Kīrtimān was the third incarnation. In his first incarnation he was known as Smara and was the son of Marīci, and later he became the son of Kālanemi. This is mentioned in the histories.

SB 10.1.68, Translation and Purport: In his previous birth, Kaṁsa had been a great demon named Kālanemi and been killed by Viṣṇu. Upon learning this information from Nārada, Kaṁsa became envious of everyone connected with the Yadu dynasty. Persons who are demons, enemies of the Supreme Personality of Godhead, are called asuras. As stated in Bhagavad-gītā, the asuras, because of their enmity toward the Supreme Personality of Godhead, take birth after birth in asura families and therefore glide down to the darkest hellish regions.

SB 10.2.4-5, Purport: The six children killed by Kaṁsa had formerly been sons of Marīci, but because of having been cursed by a brāhmaṇa, they were obliged to take birth as grandsons of Hiraṇyakaśipu. Kaṁsa had taken birth as Kālanemi, and now he was obliged to kill his own sons. This was a mystery. As soon as the sons of Devakī were killed, they would return to their original place. The devotees wanted to see this also. Generally speaking, no one kills his own nephews, but Kaṁsa was so cruel that he did so without hesitation.

Krsna Book 1: Within the prison, shackled in iron chains, Vasudeva and Devakī gave birth to a male child year after year, and Kaṁsa, thinking each of the babies to be the incarnation of Viṣṇu, killed them one after another. He was particularly afraid of the eighth child, but after the visit of Nārada, he came to the conclusion that any child might be Kṛṣṇa. Therefore it was better to kill all the babies who took birth from Devakī and Vasudeva.

This action of Kaṁsa is not very difficult to understand. There are many instances in the history of the world of persons in the royal order who have killed their father, brother or a whole family and friends for the satisfaction of their ambitions. There is nothing astonishing about this, for members of the demoniac, greedy royal order can kill anyone for their nefarious ambitions.

Kaṁsa was made aware of his previous birth by the grace of Nārada. He learned that in his previous birth he had been a demon of the name Kālanemi and that he had been killed by Viṣṇu. Having now taken his birth in the Bhoja family, he decided to become the deadly enemy of the Yadu dynasty; Kṛṣṇa was going to take birth in that family, and Kaṁsa was very much afraid that he would be killed by Kṛṣṇa, just as he had been killed in his last birth.

He first of all imprisoned his father, Ugrasena, because he was the chief king among the Yadu, Bhoja and Andhaka dynasties, and he also occupied the kingdom of Śūrasena, Vasudeva’s father. He declared himself the king of all such places.

Krsna Book 51: I have specifically taken My birth as the son of Vasudeva in the Yadu dynasty, and people therefore know Me as Vāsudeva, the son of Vasudeva. You may also know that I have killed Kaṁsa, who in a previous life was known as Kālanemi, as well as Pralambāsura and many other demons. They have acted as My enemies, and I have killed them.