The officials reiterated their opposition to US President Donald Trump's yet-to-be-announced plan for peace in the Middle East.
The trip comes as Israel celebrates the 70th anniversary of its foundation, and amid a rise in tensions between Palestinians and Israelis.
It's unclear what progress, if any, Kushner and Greenblatt made in seeking to resolve the broader dispute.
A packed schedule will also see William meet with young people, British servicemen and Syrian refugees while in Jordan.
Kushner makes no mention of Israeli settlements, the Trump administration's decision to move the US embassy in Israel to Jerusalem, or the 61 Palestinians in Gaza who Israeli forces killed that day for peacefully protesting. "They want to throw us into chaos and anarchy", said Saeb Erekat, the Palestinians' chief negotiator.
Israeli Prime Minister Benjamin Netanyahu says his talks with Kushner were productive. The U.S. ambassador to Israel, David Friedman, and Israel's ambassador in Washington, Ron Dermer, attended the meeting.
While the Gaza health ministry originally said the baby had died after inhaling tear gas, she was not included a list ministry the ministry later published of Palestinians killed by the Israel army.
Though William is not expected to comment on the long-standing conflict and stalled peace talks, his visit is being lauded by Palestinians as recognition of their occupied status. The officials said Kushner's statements had failed to convince "even one Palestinian" that the USA administration was capable of playing any role in a peace process.
Israel captured east Jerusalem from Jordan in the 1967 Mideast war and annexed it in a move not internationally recognized.
The duke will visit Ramallah in the West Bank, where he will focus on issues facing refugee communities, as well as meeting Abbas. The Palestinians consider that control a violation of any sovereignty they may gain. "If anyone walked away, it was the Trump emissaries whose plan has nothing to do with a just and lasting peace and a lot to do with normalizing the Israeli apartheid regime", he stressed. The shortfall is forcing the U.N. Relief and Works Agency to make a global emergency appeal next week.
Kushner's interview, Sha'ath said, "was the best proof that the deal of the century has failed".
The third airstrike on eastern Gaza City injured four.
Al-Quds, which publishes in east Jerusalem with an Israeli license, is the largest and oldest Palestinian newspaper.
The findings, supported by official statements from Hamas leaders, prove that Hamas was the driving force behind the deadly protests.Hamas also orchestrated several attacks at the border and encouraged Palestinians to infiltrate into Israel. Egypt and Jordan are the only Arab countries to have formal diplomatic relations with Israel.
That is keenly true for neighboring Jordan.
Official visits by British royals take place at the request of the United Kingdom government, but statements from the prince's household have given little explanation for the timing of this trip. "He has his talking points which have not changed in the last 25 years", Kushner added.
Prince William on Sunday began his first official royal visit to Israel and the Palestinian territories in a five-day tour of the Middle East.