I pray not for the world, but for them which thou hast given me; for they are thine (John 17:9) 

The above verse is sometimes used as an attempt to prove that God does not want everyone to be saved and that Jesus did not even bother to pray for all people for this reason. However, in the same chapter we can also read:

²⁰NEITHER PRAY I FOR THESE ALONE, BUT FOR THEM ALSO which shall believe on me through their word 

”The world” is often contrasted with christian believers, and often stands in relation to Satan’s dominion and to all which is evil. It is obviously not a sin to be born into this world and to live in it, but we must make sure to not live OF this world by blending in with it – or love it more than God. This present world is considered to belong to Satan and in this sense prayers for it would not accomplish much since it i represents the root of all evil. Why spend time praying for Antichrist when we already know the future result of his evil actions against God’s plans? Prayers for individuals would make more sense – that they will be able to escape the temptations of this wicked world and turn to Jesus Christ – who does not want anyone to perish. As Paul says to the Ephesians “For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world”. If all things were already determined (individuals chosen for heaven or hell before the world began), then of course there would be no reason to wrestle against anyone, nor to pray at all.

Isaiah 13:¹¹ And I will punish the world for their evil, and the wicked for their iniquity; and I will cause the arrogancy of the proud to cease, and will lay low the haughtiness of the terrible.

John 7:⁷ The world cannot hate you; but me it hateth, because I testify of it, that the works thereof are evil.

John 12:²⁵ He that loveth his life shall lose it; and he that hateth his life in this world shall keep it unto life eternal.

John 15:¹⁸ If the world hate you, ye know that it hated me before it hated you.¹⁹ If ye were of the world, the world would love his own: but because ye are not of the world, but I have chosen you out of the world, therefore the world hateth you.

Ephesians 6:¹² For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.¹³ Wherefore take unto you the whole armour of God, that ye may be able to withstand in the evil day, and having done all, to stand.

1 John 2:¹⁵ Love not the world, neither the things that are in the world. If any man love the world, the love of the Father is not in him.¹⁶ For all that is in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world.¹⁷ And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever.

1 John 5:¹⁹ And we know that we are of God, and the whole world lieth in wickedness.

Jesus is in this particular passage focusing on his disciples (apart from Judas who has already fallen), just like we sometimes focus on only some of our family members or friends in our prayers. Jesus sends his disciples on a mission to be the light of this dark world, and this of course requires lots of strength and prayers. Jesus is not giving “the world” this particular task because the world is against him and everything he stands for. The world is the reason why believers, like his disciples, need to be protected. By reading the rest of the passage (v. 2–8), we can see that those who the Father has given Jesus are those who have passed certain requirements:

• They must KNOW the only true God
• They must KEEP THE WORD
• They must RECEIVE the word
• They must BELIEVE that the Father has sent the son to the world

²As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him.³And this is life eternal, that they might KNOW thee the only true God, and Jesus Christ, whom thou hast sent.—⁶I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and THEY HAVE KEPT THY WORD.—⁸For I have given unto them the words which thou gavest me; and THEY HAVE RECEIVED THEM, and have known surely that I came out from thee, and THEY HAVE BELIEVED that thou didst send me.

Even though certain people are “given” Jesus and thus very special, they still need to be prayed for so that they will be kept and so that they may be ONE as Jesus and his Father are one in thoughts and goals. It is not a certainty that they will be kept, and we already know that Jesus lost one of his disciples given him – Judas Iscariot. Moreover, Jesus did not pray that his disciples would be taken out of this world but he prays that they will be KEPT while still living in this world. So Jesus prayers concerned his disciples who were with him (v. 12), but not all disciples were with him from the start. In. v. 20 he continues to pray also for all those who would believe on him through their words.

¹¹And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are. ¹²While I was with them in the world, I kept them in thy name: those that thou gavest me I have kept, and none of them is lost, but the son of perdition; that the scripture might be fulfilled. —¹⁵I pray not that thou shouldest take them out of the world, but that thou shouldest keep them from the evil.¹⁶They are not of the world, even as I am not of the world.

Jesus also prayed for others besides his disciples, like those who would be hearing the gospel from the mouths of the disciples.

²⁰NEITHER PRAY I FOR THESE ALONE, but for them also which shall believe on me through their word; ²¹That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me. 

One of many prophesies in the OT about Jesus is that the Messiah would be praying (make intercession) for his transgressors:

Jesaja 53:12 Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors.

Luke 23:33 And when they were come to the place, which is called Calvary, there they crucified him, and the malefactors, one on the right hand, and the other on the left. ³⁴Then said Jesus, Father, forgive them; for they know not what they do. And they parted his raiment, and cast lots.

Obviously Jesus prayed also for non-believers. If we are to believe that Jesus never prayed for anyone else but a certain lucky crowd (the elect), should we take his example and pray only for a select few? No, the Bible says that we should even pray for our enemies.

Matt. 5:⁴⁴ But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;⁴⁵ That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust.⁴⁶ For if ye love them which love you, what reward have ye? do not even the publicans the same?

You can read verses that say that Jesus died for the whole world in this blog article