"As I promised, today the work on the ground began to establish the new settlement for the settlers of Amona". "After decades, I have the privilege to be the prime minister to build a new community", he said.
A picture posted with his announcement shows construction vehicles digging up ground.
Israel is moving forward with plans for almost 4,000 housing units and has issued 2,000 tenders for settlement construction in the occupied West Bank and east Jerusalem, he added.
But Israel has not built a full-fledged new settlement since the 1990s.
Instead, construction during that period has expanded existing settlements or taken place in unauthorised outposts such as Amona. Trump condemned the decision at the time.
On the campaign trail, Mr Trump indicated he would be far more sympathetic to settlements than Mr Obama.
Palestinians regard settlements, around 200 of which have been built over the past 50 years on occupied land that they seek for a state, as obstacles to a viable and contiguous country.
Israeli and US officials provided no information on what was to be discussed and there are no plans for Kushner to speak to the media or take any questions, maintaining the circumspect profile he has established since Trump took office.
Settlements have turned the land of a future Palestinian state into a patchwork marked by Jewish-only roads, security barriers and military checkpoints. Even then, Israel's far-right government has members who are loudly opposed to peace talks as a general notion, and every move by the USA to get the talks going will be resisted every step of the way.
US mediated negotiations collapsed in 2014. Jason Greenblatt, Trump's global envoy, arrived on Monday.
Violence has subsided in recent months but last Friday an Israeli policewoman was stabbed to death in Jerusalem, with three Palestinian assailants shot dead.
Days of Palestine reports that the reduction of power to the Gaza Strip has caused a "total collapse" in all the service sectors across the tiny coastal enclave, which has been under strict Israeli siege for 11 years. They reportedly offered Hamas a quid pro quo: a more open border and a supply of electricity in return for handing over 17 men wanted by Cairo on terrorism charges, cessation of weapons smuggling into Sinai, among other demands.