Guterres pledged to act impartially as an honest broker.
While Netanyahu has made similar pledges before, the timing - on the heels of Kushner's visit and with the United Nations chief in town - gave it added significance and raised questions about his intentions for resolving the conflict with the Palestinians.
Guterres also said: "To express that the right of existence of the state of Israel doesn't exist or the wish to destroy the state of Israel is an unacceptable form of modern anti-Semitism". He said in an interview with The National published on Monday, adding that "this is the new reality that we have to accept, and there isn't much we can do about it".
Guterres landed in the Ben Gurion Airport outside Tel Aviv on Sunday night for a three-day visit, seeking to find ways to revive the peace talks between Israel and the Palestinians. I know also that the members don't always reflect their good relations with Israel that are expanding rapidly in the way that they vote in worldwide bodies.
As for attempts to bring back Israel and Palestine to the negotiations table, Guterres asked Netanyahu to work towards improving the Palestinian economy so that the Palestinians could realize the benefits of peace.
Israel law says the prime minister can only be removed by parliament, though the Supreme Court has since ruled that government ministers and mayors had to resign if indicted.
Earlier in May, UNESCO, the body's cultural agency, passed a resolution that criticised Israel's actions in occupied Jerusalem and the Gaza Strip.
Greenblatt was part of a United States delegation last week, including Trump s son-in-law Jared Kushner, that held talks with Netanyahu and Abbas.
Palestinian President Mahmoud Abbas is visiting Turkey and is not expected to meet Guterres during the trip.
The two-state solution envisions an independent Palestinian state alongside Israel, and has been the focus of worldwide diplomacy since at least the early 1990s.
Petah Tikva: Hundreds of protesters gathered in front of Israel's attorney general's home to demand he indict Prime Minister Benjamin Netanyahu on corruption charges. On Wednesday, he plans to visit the Gaza Strip.
"That is a dramatic demonstration that it is our duty to do everything possible and as Secretary General of the United Nations I fully assume that commitment to do everything possible to fight anti-Semitism in all its expressions", he said.