Education Minister Naftali Bennett, said after Trump's victory that the idea of a Palestinian state was over.
Prime Minister Benjamin Netanyahu congratulated Donald Trump on his election as US president on Wednesday and called him "a true friend of the state of Israel."
"President-elect Trump is a true friend of the state of Israel, and I look forward to working with him to advance security, stability and peace in our region," the right-wing premier said in a statement.
"The ironclad bond between the United States and Israel is rooted in shared values, buttressed by shared interests and driven by a shared destiny.
"I am confident that president-elect Trump and I will continue to strengthen the unique alliance between our two countries and bring it to ever greater heights."
Netanyahu avoided controversial topics in his statement, unlike members of his government.
Education Minister Naftali Bennett, who heads the hardline Jewish Home party, said after Trump's victory that the idea of a Palestinian state was over.
"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 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."
Others, including politicians from Netanyahu's Likud party, called for Trump to follow through on his promise to move the US embassy from Tel Aviv to Jerusalem, in a break with the consistent policy of successive administrations, Republican as well as Democrat.