In a brief statement to reporters, Canadian Foreign Minister John Baird said the ICC's decision was "deeply regretable" and would feature in his meetings with Israeli officials.
"We look forward to discussing a range of issues, from trade to security, to the deeply regretable decision at the ICC," he said before meeting Israeli counterpart Avigdor Lieberman.
The ICC said on Friday it was opening "a preliminary examination" into Israel's actions, which will cover a period including last summer's war in Gaza.
Canada played a central role in establishing the ICC and is a key supporter of the court -- a fact which was not lost on Israel.
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"We think it is completely unacceptable that a terrorist organisation like Hamas will be able to file a lawsuit against Israel," Lieberman said, standing at Baird's side.
"It's making a mockery of international law and the opposition of one of the founders of the ICC is very important, maybe crucial," he said.
Japan, whose Prime Minister Shinzo Abe is also currently visiting Israel, is the biggest financial backer of the ICC, contributing 20.4 million euros (USD 23.6 million) in 2014, according to figures up to June 30.
Canada contributed 5.6 million euros (USD 6.5 million) to the court's annual budget.
Earlier, during talks in the West Bank city of Ramallah with Palestinian foreign minister Riyad al-Malki, Baird warned against pursuing a diplomatic agenda that could prejudice the outcome of any future talks with Israel.
As he left Ramallah for Jerusalem, angry young Palestinian protestors were seen hurling eggs at his motorcade.