I have some passages that support this statement, but let me state here and now that I neither claim this to be true nor false. I make these statements from a pentecostal backgground and give what I believe to be a correct answer to the OP from the context of the OP’s question. I will also give space to scriptures which seem to dispute this in the name of fairness. I begin;
John 12:31 (NIV) Now is the time for judgment on this world; now the prince of this world will be driven out.
John 14:30 Hereafter I will not talk much with you: for the prince of this world cometh, and hath nothing in me
John 16:11 Of judgment, because the prince of this world is judged.
Eph 2:2 in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient.
2 Cor 4:4 The god of this age has blinded the minds of unbelievers, so that they cannot see the light of the gospel of the glory of Christ, who is the image of God.
1 John 4:3 and every spirit that does not confess Jesus is not from God; this is the spirit of the antichrist, of which you have heard that it is coming, and (I)now it is already in the world.
Luke 4:5–7 The devil led him up to a high place and showed him in an instant all the kingdoms of the world. 6And he said to him, “I will give you all their authority and splendor, for it has been given to me, and I can give it to anyone I want to. 7So if you worship me, it will all be yours.”
1 John 5:19 We know that we are children of God, and that the whole world is under the control of the evil one.
Matthew 4;8–10 Again, the devil took him to a very high mountain and showed him all the kingdoms of the world and their splendour. 9 All this I will give you, he said, if you will bow down and worship me. 10 Jesus said to him, Away from me, Satan! For it is written: ‘Worship the Lord your God, and serve him only.’
I have found people have two verses to dispute this. The first is:
Genesis 1:26 Then God said, “Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, [a] and over all the creatures that move along the ground.” And
Psalms 91:11–13 For he will command his angels concerning you to guard you in all your ways. 12On their hands they will bear you up, lest you strike your foot against a stone.
13 You will tread on the lion and the adder; the young lion and the serpent you will trample underfoot.
It is also stated regarding the temptation in the wilderness that Satan is the father of lies, and is therefore lying to Jesus when he offers him kingdoms in return for Jesus’ worship. The alternate point of view is that he is speaking the truth, and this is why Jesus does not refute that statement, but contends that the worship that Satan desires belongs to God alone.