Members of Prime Minister Benjamin Netanyahu’s Likud party and other rightist politicians jumped to make hay of the change.
Yoav Kish, a Likud member of Parliament, called for the expansion of Israeli sovereignty into the West Bank; Meir Turgeman, the chairman of Jerusalem’s municipal planning committee, said he would now bring long-frozen plans for thousands of Jewish homes in the fiercely contested eastern part of the city up for approval.
Aryeh Deri, the interior minister, who is ultra-Orthodox, hailed Mr. Trump’s victory as a miracle, asserting it would lessen the influence of liberal, non-Orthodox streams of Judaism popular in America. He added, “We must truly be in Messianic times when everything will turn out favorably for the people of Israel.”
Mr. Netanyahu, whose previous three terms in office all coincided with Democratic administrations in the United States, has been more cautious.
Adding to his troubles, Israel’s Supreme Court on Monday rejected a government request for a seven-month delay of the demolition of an illegal West Bank outpost built on privately owned Palestinian land. The court-ordered demolition is slated for Dec. 25, and the government had argued for the delay in part to temper a potentially violent settler response.
On Sunday, a ministerial committee of rightists within the Likud party and the governing coalition approved a contentious bill to retroactively legalize illegal settlement privately owned on Palestinian land. Prompted by the effort to salvage the Amona outpost, it may be a precursor of things to come.
Although the pro-settler camp was promoting the bill long before Mr. Trump’s victory, the decision was taken, unusually, over Mr. Netanyahu’s vehement objections and despite his exhortations for it to be postponed.
Tzipi Livni, a centrist former foreign minister and justice minister who now sits in the Parliamentary opposition, denounced the settlement bill, writing on Twitter that it constitutes “major damage to the rule of law at home, damage to Israel abroad, and primarily conveys a message that might makes right, when faced with a weak prime minister.”
Mr. Netanyahu warmly welcomed Mr. Trump’s victory, calling him “a true friend” of Israel. But Mr. Netanyahu has also since instructed his ministers and legislators to be discreet, saying the incoming administration should be allowed “to formulate — together with us — its policy vis-à-vis Israel and the region through accepted and quiet channels, and not via interviews and statements.”
Mr. Netanyahu endorsed the principle of a Palestinian state in 2009, under American pressure and with caveats. Since then, he has tried to balance between world opinion and his right-wing constituency by declaring support for a solution based on two states for two peoples without going out of his way to advance it.
Israeli analysts point out that the Trump campaign has spread contradictory messages. While many here assume that he will have more pressing priorities than the long-running Israeli-Palestinian conflict, Mr. Trump told The Wall Street Journal on Friday that he would like to seal an Israeli-Palestinian peace agreement, calling it the “ultimate deal.”
Mr. Netanyahu’s critics on the right, however, assume a Trump administration will at least give Israel a freer hand in areas like settlement construction. They say Mr. Netanyahu will have to decide which side he is on.
Acknowledging that Mr. Trump’s positions are not entirely clear, Mr. Bennett, the leader of Jewish Home, said, “We have to say what we want first.”
Amit Segal, a political commentator for Israel’s popular Channel 2 News, said that during the tenures of Presidents Clinton and Obama, Mr. Netanyahu could “disguise his worldview.” The Obama administration’s sharp condemnation of all settlement activity gave Mr. Netanyahu “the ultimate excuse” for not building with abandon in the West Bank, Mr. Segal said in an interview, adding, “I am not sure that the right wing, with its appetite, will be prepared to suffer another few years of that.”
Asked what Mr. Netanyahu would probably be rooting for, Israelis who generally reflect the prime minister’s thinking said he was unlikely to forswear the two-state solution.
“Israel has its own interest in reaching a negotiated solution with its neighbors,” said Dore Gold, a longtime Netanyahu adviser who recently resigned from his position as director general of Israel’s foreign ministry. “This is not a function of pressure or arm-twisting. Prime Minister Netanyahu has made it clear that this is his goal.”
But Mr. Gold suggested that a Trump administration was likely to roll back the demand that Israel withdraw to the 1967 lines and support borders that are more accommodating to Israel. “Trump’s policy paper spoke about Israel having defensible borders, which are clearly different from the 1967 lines,” he said.
Michael B. Oren, a deputy minister in the prime minister’s office and a former Israeli ambassador to the United States, told Israel Radio: “We have to ask ourselves what is in Israel’s interests. The interest of the Israelis and, in my view, of the government, is indeed to achieve peace with the Palestinians through direct negotiations, without preconditions, at any time, in order to get to a solution of two states for two peoples.”
Gilead Sher, an Israeli former peace negotiator under the left-leaning governments of Ehud Barak and Yitzhak Rabin, noted that although most of the Israeli governments over the past four decades had been right-wing, “never has one of them annexed one square inch of the West Bank.”
Mr. Sher, now a senior research fellow at the Institute for National Security Studies at Tel Aviv University, is also co-chairman of Blue White Future, an Israeli group advocating a two-state solution, by unilateral means if necessary. Of the rejoicing on the Israeli right, he said, “Most joyful moments are provisional and temporary.”