The three-day visit to Israel and the Palestinian territories is part of the final leg of a six-day tour of the Middle East, aimed also at promoting regional stability and peace.
The visit "gives us an historic opportunity to bring together the great capabilities of the people of Japan and the people of Israel," Israeli Prime Minister Benjamin Netanyahu told Abe in Jerusalem.
"I think there are many economic areas, technological areas and other areas in which we can cooperate," Netanyahu added.
It is the first visit by a Japanese prime minister to Israel in nine years, and Netanyahu told his cabinet it was an opportunity to continue its economic efforts in Far Eastern markets, including China and India.
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The reach to the east comes due to Israel's desire "to decrease our dependence on certain markets in western Europe," Netanyahu said.
"Western Europe is undergoing a wave of Islamisation, anti-Semitism and anti-Zionism. These waves are washing over it and we would like to ensure that the State of Israel will have varied markets around the world."
In Israel, he will hold talks with Netanyahu and President Reuven Rivlin on Monday before heading to the West Bank to meet Palestinian president Mahmud Abbas on Tuesday.
Abe is expected to call on both Israel and the Palestinians to find a way to resume peace talks which collapsed nine months ago, the embassy said.
He was also to urge Israel to refrain from any actions or remarks which would escalate the confrontation with the Palestinians.
The move was roundly denounced by both Israel and Washington, and Netanyahu is reportedly planning to discuss the move with Abe.
Japan is both a party to the ICC and its biggest financial backer. According to figures to June 30, 2014, Tokyo contributed 20.4 million euros (USD 23.6 million) to the court's yearly budget which totalled 121.6 million euros.
After Japan, the biggest contributors were Germany (13.4 million euros), France (10.5 million) and Britain (9.7 million).