Israel needs to immediately make clear that any country attempting to carry out these illegal warrants will be treated as if they attempted a kidnapping and hostage-taking of an Israeli official. And start sending Netanyahu around the world with a security force that can repel such an attempt.
Receiving countries can deny visas. Foreign citizens don't have a right to travel to other countries.
Such an action by the ICC I think would make Netanyahu persona non grata in most of Europe. They won't arrest him but that means to not having to arrest him and being exposed as hypocrites (a bunch of African states right now are salivating at the notion of European states being forced by law to arrest a foreign leader and choose not to), they just won't let him fly or travel there. The U.S. won't do anything to Netanyahu, but that's quite the long plane trip from Tel Aviv to New York and Netanyahu and his ministers would be even more effectively isolated internationally.
If Netanyahu flies to the U.S. and he is under ICC criminal charges and we choose to do nothing, then the U.S. can never say anything "ICC" again in any circumstance and have it be worth ten cents.
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Any country who is a signatory to the Rome Statute would be obliged to arrest him.
Didn't really work in South Africa with the Sudanese leader did it?
That would be a middle ground that would likely still have severe diplomatic consequences, both with Israel and the US, but not nearly the dangerous pandora's box that would ensue if any of these countries tried to detain Netanyahu or Gallant.