"We are told by the Israeli media that Prime Minister Netanyahu, whom I met repeatedly, wants to cancel this meeting just because we meet with critical representatives of civil society", Gabriel told German public television.
Israeli Environment Minister Zeev Elkin, a confidante of Netanyahu, told Israel radio it was "unthinkable" for a minister to meet groups working against the country he was visiting. But he said a cancellation of Tuesday's meeting would not be a "catastrophe", and wouldn't change his relationship with Israel.
"You never get the full picture of any state in the world if you meet only with government officials", he said. But when Netanyahu called, the minister did not answer.
Prime Minister Benjamin Netanyahu meets with Austrian Chancellor Christian Kern at the Prime Minister's Office in Jerusalem, on April 25, 2017.
Interior Minister Rabbi Aryeh Deri said that Mr. Netanyahu had his "full support".
Gabriel arrived in Israel on Monday to participate in Holocaust Remembrance Day events and meet with local leaders.
Gabriel, for his part, insisted that his desire to meet with critics of the government was nothing out of the ordinary, and characterized Mr. Netanyahu's cancellation as "exceptional" and "regrettable".
The spat follows Netanyahu's demand to Theresa May during an official visit to London that the British government cease funding Breaking the Silence, despite the fact it is not a recipient of direct British aid. Identifying that common interest is the first step in real negotiations, in which Germany and Europe could assume an important role.
Rivlin also mentioned renewable green energy, a topic of importance to Gabriel, Germany's minister of the environment until January of this year, and formerly is federal minister for economic affairs and energy. He would have rather discussed Israel's arch nemesis, Iran, and the larger regional conflict in the context of war in Syria and global terrorism. "You have to talk to writers, artists and students, and also with critical organizations".
In February, Belgium's ambassador to Israel Olivier Belle was summoned for a dressing down in the Foreign Ministry over a meeting by his country's prime minister, Charles Michel, with representatives of the two NGOs.
Earlier this month, however, two former heads of Israel's Shin Bet domestic intelligence agency publicly defended the group's right to speak out.
Breaking The Silence seeks to document Israeli military abuses in the Palestinian territories, while B'Tselem has worked on a range of issues and has strongly opposed Israeli settlement building.