"About 500,000 Jews live in about 140 settlements built since Israel's 1967 occupation of the West Bank and East Jerusalem.
The settlements are considered illegal under international law, although Israel disputes this.
Most of the new homes approved on Tuesday will be built in existing West Bank settlement blocs, including 902 in Ariel and 652 in Givat Zeev.
One hundred will be constructed in Beit El, a settlement near Ramallah that reportedly has received funding from a foundation run by the family of Mr Trump's son-in-law and senior adviser, Jared Kushner.
Following the announcement, Mr Netanyahu declared on Twitter: "We are building - and continuing to build."
http://www.bbc.co.uk/news/world-middle-east-38740712