Israel seized the West Bank and east Jerusalem in 1967. It later annexed east Jerusalem in a move never recognised by the international community.
The Palestinians see east Jerusalem as the capital of their future state, while Israel views the entire city as its capital.
Some 400,000 Israeli settlers now live in the West Bank, with another 200,000 in east Jerusalem.
In comparison, about 2.9 million Palestinians live in the West Bank and east Jerusalem.
Netanyahu currently heads what is seen as the most right-wing government in Israeli history and faces strong pressure from the settlement movement to expand construction.
On Monday, he spoke of the advantages the Trump presidency could provide, but also called for restraint.
Education Minister Naftali Bennett of the hardliner Jewish Home party has been among those pushing for immediate moves, such as the unilateral annexation of a large West Bank settlement near Jerusalem called Maale Adumim.
Trump also vowed during his campaign to recognise Jerusalem as Israel’s capital and move the US embassy to the city from Tel Aviv.
The move would constitute a break with decades of precedent and be in opposition to nearly all of the international community.
The White House has however since seemed to downplay the promise, saying it was only at the beginning stages of discussing such a move.