It also asked the court to suspend the execution of the warrants for the two pending the outcome of the appeal.
Israel disputes the jurisdiction of the tribunal and the legitimacy of issuing arrest warrants, the prime minister's office said, adding that a rejection of the request would prove again how hostile the tribunal is to Israel.
The tribunal did not immediately comment on Israel's appeal policy, AFP said, only stating its principled position that the justices would judge if an appeal was received.
Earlier, since October 8 last year, the ICC has issued arrest warrants for Netanyahu and former Minister Galant on charges of committing crimes against humanity and war crimes in Gaza, Palestine.
The ICC also issued a warrant for the arrest of Muhammad Daif, commander of the Hamas militant al-Qassam brigade.
Daif is said to have been killed in an Israeli airstrike, but Hamas has not confirmed it.
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