It is the Gentiles' obligation to provoke Israel to jealousy. Paul spoke more on this.
Romans 11:13-15 (KJV)
For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
If by any means I may provoke to emulation them which are my flesh, and might save some of them.
For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead?
In verse 13 Paul stated that while he was speaking to Gentiles, because he was the apostle of the Gentiles, his work was visible and open to the Jews. By teaching and preaching to the Gentiles he believed that he would provoke the Jews to emulate the believers and some might then be saved (verse 14).
Paul then reiterated that if the Jews' temporary rejection of Messiah meant reconciliation between the world (Gentiles) and God, how much more would be accomplished by the Jews receiving Messiah in faith? Ultimately, it would mean the salvation of the Jews, not only individually, but nationally, as well.
Stay tuned for more!