Kushner, a 36-year-old real estate developer with little experience of worldwide diplomacy or political negotiation, arrived in Israel on Wednesday morning and will spend barely 20 hours on the ground - he leaves shortly after midnight.
Kushner and the US ambassador to Israel, David Friedman, visited the family of Hadas Malka, Ynet reported.
Kushner replied: "The president sends his best regards and it's an honour to be here with you".
Kushner is in the country along with special envoy Jason Greenblatt to try to promote Trump's plan for a peaceful solution to the Israeli-Palestinian conflict.
"He offered the condolences to the bereaved family from the U.S. president, who spoke to his son-in-law on the way and asked that he be kept updated about the visit", a close friend of the Malka family told Israel's Ynet news.
More than 600,000 Israelis live in settlements in the West Bank, including annexed East Jerusalem, which are seen as a major obstacle to peace between Israel and Palestinians.
Greenblatt is to be joined by Trump's son-in-law and adviser Jared Kushner on Wednesday.
But when he met Netanyahu in Washington in February, Trump 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".
Trump has asked Netanyahu to hold back on settlement building as he seeks to build momentum for a new peace push. During their visit, the two are expected to visit Jerusalem and Ramallah.
Since then, conversations have been ongoing, the White House official said.
"Those who want to make it harder rather than easier to make peace, whether by their statements or their actions, must be prevented from subverting the chances for peace", the official said.
Those issues have always been thorny problems in the multiple rounds of peace negotiations launched by both Republican and Democratic presidents since the mid-1990s.