Several nations, including Italy and the Netherlands, said on Thursday that Mr Netanyahu and Mr Gallant would be arrested if they entered their countries.
Guido Crosetto, Italy’s defence minister, told RAI television: “We would have to arrest them.”
He added that it was not a political choice but that Italy was bound as a member of the ICC to act on the court’s warrants.
The Netherlands also said it would comply with the arrest warrants.
It followed a call by the European Union on its member states to respect and comply with the arrest warrants following the ICC’s landmark decision.
The EU’s foreign policy chief, Josep Borrell, also disputed Israel’s claim that the court’s decision was political.
‘Not political’
“It is not a political decision. It is a decision of a court, of a court of justice, of an international court of justice. And the decision of the court has to be respected and implemented,” Mr Borrell said, adding that the court’s decision is binding on all EU member states.
Other European countries expressed their support for the ICC decision.
Simon Harris, Ireland’s prime minister, called the decision an “extremely significant step. These charges could not be more serious”.
“Ireland respects the role of the International Criminal Court. Anyone in a position to assist it in carrying out its vital work must now do so with urgency,” added Mr Harris.
But France’s foreign ministry stopped short of saying that Mr Netanyahu and Mr Gallant would be arrested if they set foot on French soil.
“It’s a point that is legally complex so I’m not going to comment on it today,” a spokesman said.
Beyond Europe, Justin Trudeau, the prime minister of Canada, said his government will abide by all the regulations and rulings of the International Criminal Court.
He said: “It’s really important that everyone abides by international law. We stand up for international law, and we will abide by all the regulations and rulings of the international courts.”
Ayman Safadi, Jordan’s foreign minister, also said the ICC’s ruling must be respected by its member states.