Was Jesus Only Sent To Israel?

Muslims often use the argument that Jesus was only sent to Israel, while Mohammed and the Quran was sent to the whole world.  Therefore Mohammed supersedes Jesus.

Here are some verses they give as evidence:

⁵ Jesus sent out these twelve after giving them instructions: 
“Don’t take the road leading to other nations, and don’t enter any Samaritan town. 
⁶ Instead, go to the lost sheep of the house of Israel.
--Matthew 10:5

[Jesus] replied, “I was sent only to the lost sheep of the house of Israel.”
--Matthew 15:24

This may be convincing in the Muslim mindset, where Jesus is one in a series of prophets, each to different people groups. but Christians regard Jesus as a prophet only incidentally.  

However, we believe that Jesus made atonement for the sin of the whole world, and thereby fundamentally changed the relationship between God and Man (John 3:16).  Consistent with most other Old Testament prophets, his message was primarily directed at the Jewish people.  His disciples were given the job of proclaiming the gospel to the world.

Jesus directly says his work does is not just for the Jews of his time:

14 I am the good shepherd. I know My own sheep, and they know Me, 
¹⁵ as the Father knows Me, and I know the Father. I lay down My life for the sheep. 
¹⁶ But I have other sheep that are not of this fold; I must bring them also, and they will listen to My voice. Then there will be one flock, one shepherd.
--John 10:14-16

Also, if the message of Jesus was only limited to Israel, that would make us ask what the meaning of the following verse is:

  ¹⁴ This good news of the kingdom will be proclaimed in all the world as a testimony to all nations. And then the end will come.
--Matthew 24:14

It was Peter's vision in Acts 10:19 that caused the early Jewish Christians to realize they had to proclaim this message to the world.