The arrest warrants issued by the International Criminal Court are the first time that leaders of a modern Western democracy have been accused of war crimes and crimes against humanity by a global judicial body.

By themselves, the warrants, seeking the arrests of Prime Minister Benjamin Netanyahu of Israel and his former defense minister, Yoav Gallant, represent an important diplomatic landmark. They will be seen by many countries in the global south, rightly or wrongly, as a sign that international institutions are no longer necessarily tools of the West.

While the United States and Israel are not signatories to the court, more than 120 nations are, and they are formally committed to carrying out the arrest warrants if Mr. Netanyahu, Mr. Gallant or any other wanted person steps on their soil, even if by accident, like a plane malfunction requiring an unscheduled landing.

The arrest warrants “are binding on all parties to the I.C.C.,” said Philippe Sands, an expert in international law who has argued before the court. “If they set foot on the territory of a state party, that state party has an obligation to arrest and transfer to The Hague. That’s pretty binding.”

But states do not always comply, especially when powerful countries are involved. Mongolia, an I.C.C. member deeply dependent on Russia for fuel, not only did not arrest its president, Vladimir V. Putin, who is wanted by the court on charges of war crimes stemming from Russia’s invasion of Ukraine, it greeted him with an official state ceremony in September. South Africa, another I.C.C. member, avoided the dilemma of whether to arrest him last year when he decided not to attend a large summit in person.

And while President Luiz Inácio Lula da Silva of Brazil had said that there was “no reason” that Mr. Putin should fear attending the Group of 20 summit in Rio de Janeiro this year, Mr. Putin sent his foreign minister instead.