The only place where the 1,000 years are mentioned is in Revelation 20. Show me in the prophets where a specific reference to a future 1,000-year period occurs. There are none. It seems to me that people have tried to fit all the references about peace in the future into the future millennium. Rather, I think those references fit much better the final kingdom on the new earth, to which the new Jerusalem descends in Revelation 21 and 22.
Another more compelling interpretation is also that the end of Revelation 19 symbolically describes Jesus' second coming, and the next chapter begins a new vision that describes the present age symbolically as 1,000 years, in which God prevents Satan from hindering the spread of the gospel.
Of course, we can all be pan-millennialists, that is, it'll all pan out!
Rev 20:1 Then I saw an angel coming down from heaven, holding in his hand the key to the bottomless pit and a great chain.
Rev 20:2 And he seized the dragon, that ancient serpent, who is the devil and Satan, and bound him for a thousand years,
Rev 20:3 and threw him into the pit, and shut it and sealed it over him, so that he might not deceive the nations any longer, until the thousand years were ended. After that he must be released for a little while.
Rev 20:4 Then I saw thrones, and seated on them were those to whom the authority to judge was committed. Also I saw the souls of those who had been beheaded for the testimony of Jesus and for the word of God, and those who had not worshiped the beast or its image and had not received its mark on their foreheads or their hands. They came to life and reigned with Christ for a thousand years.
Rev 20:5 The rest of the dead did not come to life until the thousand years were ended. This is the first resurrection.
Rev 20:6 Blessed and holy is the one who shares in the first resurrection! Over such the second death has no power, but they will be priests of God and of Christ, and they will reign with him for a thousand years.
Rev 20:7 And when the thousand years are ended, Satan will be released from his prison
Rev 20:8 and will come out to deceive the nations that are at the four corners of the earth, Gog and Magog, to gather them for battle; their number is like the sand of the sea.