Kushner, a 36-year-old real estate developer with little experience of international diplomacy or political negotiation, arrived in Israel on Wednesday morning and was due to spend barely 20 hours on the ground.
After a meeting with Prime Minister Benjamin Netanyahu, Kushner travelled to Ramallah where he held two hours of talks with Palestinian President Mahmoud Abbas after iftar, the evening meal that breaks the daily Ramadan fast.
Abbas spokesman Nabil Abu Rdainah said all major issues at the heart of the conflict were discussed.
In discussions with Greenblatt before Kushner's visit, Palestinian sources said the phrase "two-state solution" had not been used.
Palestinian sources said that ahead of Kushner's meeting with Abbas, they had been asked to draw up a list of 12 "bullet point" demands they would want met in any negotiations.
Earlier, video showed him giving Israeli Prime Minister Benjamin Netanyahu, a friend of Kushner's father, a handshake and a hug as they prepared to sit down with the Israeli ambassador to Washington, the US ambassador to Israel and other senior officials for preliminary discussions.
"This is an opportunity to pursue our common goals of security, prosperity and peace," Netanyahu said. "Jared, I welcome you here in that spirit. I know of your efforts, the president's efforts, and I look forward to working with you to achieve these common goals."
Kushner replied: "The president sends his best regards and it's an honour to be here with you."
Kushner did not speak to the media or take questions, maintaining the circumspect profile he has established since Trump took office in January.
US officials and Israeli leaders "underscored that forging peace will take time and stressed the importance of doing everything possible to create an environment conducive to peacemaking," the White House later said in a statement.
US officials called the trip part of an effort to keep the conversation going rather than the launching of a new phase in the peace process, saying that Kushner and Jason Greenblatt, the president's special representative for international negotiations, are likely to return often.
Trump has described peace between the Israelis and the Palestinians as "the ultimate deal" and made it a priority. As well as receiving both Netanyahu and Abbas in the White House, he visited the region last month.
When Trump met Netanyahu in Washington in February, he said he was not fixed on two states saying, "I'm looking at two-state and one-state, and I like the one that both parties like".