The Palestinian Authority (PA) government said on Thursday in a statement that the court's decision "restores hope and confidence in international law and its institutions, and in the importance of justice, accountability and the prosecution of war criminals".
The PA is headquartered in the Israeli-occupied West Bank city of Ramallah and exercises nominal self-rule in parts of the territory.
The criminal court released arrest warrants for Netanyahu and Gallant on Thursday, accusing them of war crimes in Gaza - where more than 44,000 Palestinians have been killed since Israel launched its campaign, according to the Palestinian Health Ministry.
The ICC said it had found "reasonable grounds" to believe Netanyahu and Gallant bore "criminal responsibility" for the war crime of starvation as a method of warfare, as well as the crimes against humanity of murder, persecution, and other inhumane acts.
The statement from the Palestinian Authority, which has partial administrative control in the Israeli-occupied West Bank, did not make any mention of the warrant also issued on Thursday for Hamas's military chief Mohammed Deif over war crimes and crimes against humanity.
Israel said it killed Deif in Gaza in July, but Hamas has not confirmed his death.
The group, in its own statement about the ICC decision, similarly did not mention Deif.
Hamas said the warrants for the Israeli leaders were "an important step towards justice and can lead to redress for the victims in general".
"But it remains limited and symbolic if it is not supported by all means by all countries around the world", the group's political bureau member Bassem Naim said.
Husam Zomlot, the Palestinian ambassador to the UK, said it was "incumbent upon all parties" to enforce the ICC measures. While the court cannot enforce arrests, signatory states are obliged to apprehend those facing warrants.
"The ICC arrest warrants against Netanyahu and Gallant is not only a step towards accountability and justice in Palestine but also a step to restore the credibility of the rules-based international order and its judicial system," he posted on X.