Conservative groups that oppose Solicitor General Elena Kagan’s Supreme Court nomination are hoping that her statement of support for Israeli Supreme Court Chief Justice Aharon Barak will become a flash point in her confirmation hearings, which start Monday.

As video of Kagan’s introduction of Barak circulated online Wednesday, organizations like anti-abortion group Americans United for Life and the Traditional Values Coalition used the Kagan-Barak connection, in the absence of any written legal decisions by Kagan, to bolster their argument that she would be an activist judge if confirmed.

According to Traditional Values Coalition Executive Director Andrea Lafferty, Kagan has indicated her willingness to use international law in interpreting U.S. cases, which Lafferty said is a pillar of Barak’s judicial philosophy...