"Those who are demons, those who are sinful, nature's law is to place him in such condition that he will become more and more a demon so that he will never be able to understand what is God. This is nature's law. If you want to forget God, then God will put you in such a condition that you can never understand what is God. That is demonic life. That time is also coming. At the present moment, still a few men are interested, what is God. Arto artharti jijnasu jnani. But time is coming ahead when there will be no sense to understand God. That is the last stage of Kali-yuga, and at that time Kalki avatara, Kalki avatara will come. At that time there is no preaching of God consciousness, simply killing, simply killing. Kalki avatara with His sword will simply massacre. Then again Satya-yuga will come. Again golden age will come."
Srila Prabhupada Lecture, 08-06-73, London
"Thereafter, at the conjunction of two yugas, the Lord of the creation will take His birth as the Kalki incarnation and become the son of Visnu Yasa. At this time the rulers of the earth will have degenerated into plunderers.
Purport: Here is another foretelling of the advent of Lord Kalki, the incarnation of Godhead. He is to appear at the conjunction of the two yugas, namely at the end of Kali-yuga and the beginning of Satya-yuga. The cycle of the four yugas, namely Satya, Treta, Dvapara and Kali, rotates like the calendar months. The present Kali-yuga lasts 432,000 years, out of which we have passed only 5,000 years after the Battle of Kuruksetra and the end of the regime of King Pariksit. So there are 427,000 years balance yet to be finished. Therefore at the end of this period, the incarnation of Kalki will take place, as foretold in the Srimad-Bhagavatam. The name of His father, Visnu Yasa, a learned brahmana, and the village Sambhala are also mentioned. As above mentioned, all these foretellings will prove to be factual in chronological order. That is the authority of Srimad-Bhagavatam."
"In Vedic literature there are names like mleccha and yavana. The mlecchas are understood to be those who do not follow the Vedic principles. In former days, the mlecchas were fewer, and Visvamitra Muni cursed his sons to become mlecchas. But in the present age, Kali-yuga, there is no need of cursing, for people are automatically mlecchas. This is only the beginning of Kali-yuga, but at the end of Kali-yuga the entire population will consist of mlecchas because no one will follow the Vedic principles. At that time the incarnation Kalki will appear. Mleccha-nivaha-nidhane kalayasi kara-balam. He will kill all the mlecchas indiscriminately with his sword."
Srimad-Bhagavatam 9:16:33 Purport
"The next avatar incarnation is Kalki. That is yet to take place. Kalki avatara will appear at the end of this age, Kali- yuga. The age of Kali-yuga, duration of this age is still to be, I mean to say, fulfilled in 400,000's of years. So at the end of Kali, that means at the last stage, after about 400,000's of years, the incarnation of Kali will appear. That is predicted in the Vedic literatures, as Lord Buddha's appearance was also predicted in the Srimad-Bhagavatam. And Srimad-Bhagavatam was compiled five thousand years ago, and Lord Buddha appeared about 2,500 years ago. Therefore about Lord Buddha's appearance it is predicted that at the beginning of Kali-yuga Lord Buddha will appear. There was prediction, and that has actually come to be true. Similarly, there is prediction about Kalki avatara, and that will also come to be true. So at that time Lord Kalki's business will be simply to kill. No instruction. Just like... In Bhagavad- gita Lord Krsna gave instruction in the shape of Bhagavad-gita. But at the end of Kali-yuga, people will be so much degraded that there is no more possibility to give any instruction. They will not be able to understand even. At that time the only weapon will be to kill them. And one who is killed by the Lord, he also gets salvation. That is God's all-merciful quality. Either He protects or He kills, the result is the same. So that will be the last stage of this Kali-yuga, and after that, again Satya-yuga, the age of religiosity, will begin. These are the statements of Vedic literature."
Srila Prabhupada Lecture, 02-18-70, Los Angeles
Bhaktivedanta Book Trust. Excerpted from texts and purports of HDG A.C. Bhaktivedanta Swami Srila Prabhupada.