Mr Kushner said “the stage is set” for other Arab states to follow suit but gave no indication that any new deals were imminent.
Appearing alongside Israeli Prime Minister Benjamin Netanyahu and the US national security adviser Robert O’Brien, Mr Kushner spoke a day before he is to join a senior Israeli delegation on the first commercial flight from Israel to the UAE.
The flight holds great symbolic value and is a key step in what is expected to be full normalisation between Israel and the UAE.
The August 13 announcement makes the UAE the third Arab country to establish full diplomatic relations with Israel, and the first to do so in over 25 years.
It reflects a shifting Middle East in which shared concerns over Iran have overtaken traditional wall-to-wall Arab support for the Palestinians.
“Today obviously we celebrate a historic breakthrough for peace,” Mr Kushner said, adding that the deal will create “previously unthinkable” economic, security and religious co-operation.
“While this peace agreement was thought by many to be impossible, the stage is now set for even more,” he said.
“We must seize that optimism and we must continue to push to make this region achieve the potential that it truly has.”
Israel and the UAE have moved quickly to cement their ties over the past two weeks. Almost immediately, they opened direct phone lines, and Cabinet ministers have held phone conversations.
On Saturday, the UAE formally ended its commercial boycott of Israel, although the two countries have quietly conducted business for years.
Monday’s flight of an El Al plane from Tel Aviv to Abu Dhabi will be the first known flight of an Israeli commercial airliner from Israel to the Emirates.
The two Middle East countries are expected to sign a formal agreement at the White House in the coming weeks.
But so far, predictions by Israeli and American officials, including Mr Kushner, that other Arab countries would follow the UAE have not yet materialised.
US Secretary of State Mike Pompeo toured the region last week, stopping in Sudan, Bahrain and Oman — three countries widely seen as candidates to establish ties with Israel — but appeared to leave empty-handed.
The flurry of US diplomatic activity comes as the Trump administration presses ahead with ambitious plans to promote Arab-Israeli rapprochement even in the absence of a settlement to the Israeli-Palestinian conflict, which had long been seen as a prerequisite for Israel to reach peace deals with all of its Arab neighbours.
Mr Netanyahu said the agreement with the UAE would bring “unbridled” trade and opportunities.