The new settlement - the first since 1992, according to Israeli NGO Peace Now - is meant to house residents of the illegal West Bank outpost of Amona after the Israeli military demolished it in February.
The construction work comes despite a request by Trump at a meeting between the two men in Washington this year to "hold back on settlements for a little bit" - a comment seen as part of an effort to build trust with the Palestinians, but greeted by many with deep scepticism. He appears to have backtracked since.
Israel for decades has pursued a policy of constructing Jewish settlements on territory captured by Israel in the 1967 war with its Arab neighbours.
Greenblatt, President Donald Trump's special envoy to the Middle East, arrived Sunday in Israel.
The Amichai settlement will be the first new government-sanctioned Jewish settlement in the Palestinian territories in some 25 years.
"Such construction continues to distance us from the only way to end the Israeli-Palestinian conflict - a two-state solution".
Trump has made it clear that working toward achieving a lasting peace agreement between the Israelis and Palestinians is a top priority for him, a White House official told CNN ahead of Kushner's arrival.
Mladenov was delivering the second report on implementation of the resolution adopted by the council in December condemning Israeli settlements as a "flagrant violation" of global law.
Building settler homes in the Israeli-occupied West Bank soared 70 percent in 2017 to March, data released by the Central Bureau of Statistics showed today. "They are a risky actor who has no care for the Palestinians, no care for the Israelis, and they are determined to destroy everything in their path", Haley said. Israel also cites biblical, historical and security interests to defend settlements.