Right-wing Hungarian Prime Minister Viktor Orban invited his Israeli counterpart to Budapest in November, a day after the ICC issued its arrest warrant over allegations of war crimes in Gaza, where Israel launched its offensive following an attack by Hamas-led fighters on southern Israel.
Israel has rejected the accusations, which it says are politically motivated and fuelled by anti-Semitism.
It says the International Criminal Court has lost all legitimacy by issuing the warrants against a democratically elected leader of a country exercising the right of self defence.
As a founding member of the ICC, Hungary is theoretically obliged to arrest and hand over anyone subject to a warrant from the court but Orban made clear that Hungary would not respect the ruling which he called "brazen, cynical and completely unacceptable".
On Thursday, Gergely Gulyas, Orban's chief of staff, told state news agency MTI that the government would launch the withdrawal process later in the day.
Orban had raised the prospect of Hungary's exit from the ICC after US President Donald Trump imposed sanctions on the court's prosecutor Karim Khan in February.
"It's time for Hungary to review what we're doing in an international organisation that is under US sanctions," Orban said on X in February.
The bill on starting the year-long process of withdrawing from the ICC is likely to be approved by Hungary's parliament that is dominated by Orban's Fidesz party.
Netanyahu has enjoyed strong support from Hungary's Orban, an important ally who has been ready to block EU statements or actions critical of Israel in the past.
ICC judges said when they issued the warrant that there were reasonable grounds to believe Netanyahu and his former defence chief were criminally responsible for acts including murder, persecution and starvation as a weapon of war as part of a "widespread and systematic attack against the civilian population of Gaza".
The Israeli campaign has killed more than 50,000 Palestinians, according to Palestinian health authorities, and devastated the Gaza Strip.
The Hamas-led attack on Israel on October 7, 2023, killed 1200 people and saw more than 250 taken hostage, according to Israeli tallies.