Kushner's visit comes a month after he escorted Trump to Israel.
Prime Minister Benjamin Netanyahu presented the news of the groundbreaking on Twitter. Some 100 housing units are planned.
Just before Kushner's trip, Israel began construction on a new settlement in the West Bank, the first new outpost there in 25 years.
U.S. officials, including Secretary of State Rex Tillerson, have said that they are pushing Abbas to end incitement to violence against Israel, and to stop paying stipends to terrorists and their families.
While Kushner may have no direct experience in diplomacy, he is qualified for his role by virtue of his family's long friendship with Israeli Prime Minister Netanyahu, and by his role as a director of a family foundation that has made charitable donations to West Bank settlements.
US Special Representative for International Negotiations Jason Greenblatt and US Consul General in Jerusalem Donald Blome also attended the meeting, which the Americans stated was "positive and fruitful".More news: Foreign investors bet billions on China blue-chips joining MSCI index
It is being built for the roughly 40 families evicted from the wildcat outpost of Amona earlier this year after Israel's high court ruled their homes had been built illegally on private Palestinian land. Hadas Malka was serving in the Israeli border patrol when she was fatally stabbed (another Israeli suffered minor injuries).
United States ambassador, Jason Greenblatt expressed outrage over Malka's death.
"This is an opportunity to pursue our common goals of security, prosperity and peace", Netanyahu told the Trump aides. However, the Palestinian president received no promises in this regard.
A day after meeting the Americans, Abbas defended payments to Palestinian prisoners, including convicted terrorists, as "social responsibility" and accused Israel of trying to sabotage peace negotiations with unreasonable demands. Abbas' spokesman, Nabil Abu Rudaineh, said that the two men held a detailed discussion that focused on issues at the core of a final status agreement. "There will never be another Prime Minister who makes propositions to Palestinians like Ehud Olmert did", he added, referring to a 2008 peace proposal introduced by the former prime minister.
Kushner joined by U.S. Mideast envoy Jason Greenblatt and Ambassador David Friedman met for two and a half hours with the Israeli leader before going to Ramallah for talks with Abbas, the newspaper said.