"Trump's victory is an opportunity for Israel to immediately retract the notion of a Palestinian state in the centre of the country, which would hurt our security and just cause," Bennett, who heads the hardline Jewish Home party, said in an apparent reference to the occupied West Bank.
"This is the position of the president-elect ... The era of a Palestinian state is over."
Deputy Foreign Minister Tzipi Hotovely, from Prime Minister Benjamin Netanyahu's right-wing Likud party, also called for the embassy to be moved, as did Jerusalem Mayor Nir Barkat.
There was no immediate reaction from Netanyahu himself.
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The prime minister caused controversy when he ruled out a Palestinian state ahead of a 2015 general election, but later backtracked and has since expressed support for the two-state solution.
The Palestinians see east Jerusalem as the capital of their future state, while the Israelis call the entire city their eternal indivisible capital.
Trump has pledged to recognise Jerusalem as Israel's capital.