Earlier, Abe met Palestinian Prime Minister Rami Hamdallah in the West Bank city of Jericho and toured an agricultural park supported by Japan.
The prime minister told Abe that the Iranian nuclear deal was "a bad agreement based on the lies and scams of Iran".
The protests are meant to last six weeks, ending in mid-May, around the time the United States will move its embassy in Israel from Tel Aviv to Jerusalem.
Abe also urged Israel to refrain from building new settlements in Palestinian territory.
The two state leaders agreed to move forward on the issue of direct flights from Japan to Israel, which would increase tourism, investments and business.More news: Vikings Exercise 5th-Year Option for Trae Waynes
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This week's visit to the Middle East by Prime Minister Shinzo Abe was made to show indirect support for USA diplomatic efforts toward regional peace, sources said. "And also I am very happy to note that there has been the dramatic increase in the Japanese investment to Israel under my administration", he said. He is accompanied by his wife and a delegation of senior Japanese business leaders.
Abe added that "I brought a business delegation from Japan to Israel, which includes so numerous CEO's from Japan, so I do hope that you'll have a productive discussion with the business leaders in the summit meetings that we are planning to have". In 2017 alone there were 50 investments by Japanese companies in Israeli companies, the PMO said.
"This is your second visit to Israel".
The Center for Constitutional Rights said in a statement Tuesday that the trip was created to help participants "better understand the human rights situation in Israel and Palestine, including the history of systematic displacement and institutional racism, as well as the work of human rights defenders there".
Abe thanked Netanyahu for his hospitality and invited the prime minister to make a reciprocal visit in Japan in the coming year. "This is a good partnership and we will strengthen it even more".