"After dozens of years, I have the privilege to be the prime minister building a new settlement in Judaea and Samaria", Netanyahu tweeted, using the Hebrew biblical term for the West Bank.
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.
On the campaign trail, Trump indicated he would be far more sympathetic to settlements than Obama. He appears to have backtracked since.
The expansion of existing settlements on the West Bank - territory which Israel occupied during a conflict in 1967, has been a major point of contention in the Israeli-Palestinian conflict.
Jared Kushner, the president's son-in-law and senior adviser, and Jason Greenblatt, his lead global negotiator, will meet with leaders from both sides after accompanying Trump on his visit to the region last month.
In the past, Israel has not announced or started major construction projects in the West Bank while senior USA officials were visiting.
Amichai marks the first state-approved settlement in the West Bank since the signing of the Israeli-Palestinian Oslo peace accords in 1993.
Trump has described peace between the Israelis and the Palestinians as "the ultimate deal" and made it a priority since taking office.
But Israel has continued to provide limited power to Gaza, paid for by the Palestinians, to prevent a humanitarian crisis on its doorstep and out of concern that more instability could lead to renewed fighting.
Discussions have been ongoing since that May 22 trip, the official said. White House officials played down expectations of a dramatic breakthrough during the visit, the New York Times reported.
Regardless of whether a state chooses to support Israel or Palestine, "pitting the two sides against each other is only strengthening the terrorists", she said.
Nickolay Mladenov stressed that the United Nations considers settlement activities illegal under worldwide law.
"The large number of settlement-related activities documented during this period undermine the chances for the establishment of a viable, continuous Palestinian state as part of a two-state solution", he said.
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. He has also said settlements are not a core problem of the Israeli-Palestinian dispute.