Naftali Bennett, leader of the religious-nationalist Jewish Home party and a staunch proponent of Israeli settlement building, said it was now up to Prime Minister Benjamin Netanyahu to communicate to the U.S. administration and the world what he wanted and push for it.
Referring to his own past as a high-tech entrepreneur, Bennett said not making the goals clear would result in failure.
"The combination of changes in the United States, in Europe and in the region provide Israel with a unique opportunity to reset and rethink everything," Bennett, 44, told members of the Foreign Press Association.
"We have a chance to reset the structure across the Middle East. We have to seize that opportunity and act on it."
Relying on "old paths", he said, would be a mistake.
Bennett would not be drawn on what actions he thinks Netanyahu should take. But in the past, Bennett has called for the annexation of most of the West Bank, which the Palestinians want for a state together with Gaza and East Jerusalem.
Israel has occupied the West Bank and East Jerusalem since the 1967 Middle East war.
Netanyahu, who has a fractious relationship with President Barack Obama, has welcomed Trump's election, chatting with him by phone and posting a video on Facebook promoting the ties between the countries. Their wives have also spoken.
But he has also been cautious about over-playing the benefits of a Trump presidency, perhaps so as not to preempt whatever policies the president adopts and to avoid giving the impression that he expects something from the United States.
During the campaign, however, Trump made it clear he would support Israel in a number of critical areas, including moving the U.S. embassy from Tel Aviv to Jerusalem, all but enshrining Jerusalem as Israel's capital over international objections, and not applying pressure for talks with the Palestinians.
Jason Greenblatt, an adviser to Trump on the Middle East, has also said that Israeli settlements built on land the Palestinians want for their own state are not an obstacle to peace and that the two-state solution - the bedrock of international diplomacy for 20 years - is not working.
As a result, many Israeli politicians and analysts have concluded that a Trump presidency will be a boon for Israel. Palestinian officials are reluctantly drawing the same conclusion, and have urged the world to pay attention.
Immediately after Trump's victory, Bennett declared that the two-state solution - the idea of a Palestinian state side-by-side with Israel and at peace - was effectively dead.
"Trump's victory is an opportunity for Israel to immediately retract the notion of a Palestinian state," he said. "The era of a Palestinian state is over."
He wouldn't reiterate that point on Monday, but did say "it's no secret that I think the idea of setting up a Palestinian state in the heart of Israel is a mistake."
Netanyahu has said he supports a negotiated settlement that leads to a demilitarized Palestinian state. But he opposes any return to pre-1967 lines, which he says would be indefensible, and demands Palestinians recognize Israel as a Jewish state in any peace deal. Talks between the sides collapsed in 2014.
While Bennett and others may be excited at the prospect of Trump in the White House, it is possible some of his policy ideas will be toned down between now and taking office. Presidential candidates have in the past promised to move the U.S. embassy to Jerusalem and then reneged.
The other consideration for both Israel and the new U.S. administration is the risk of serious fallout from an overly pro-Israel policy. If it becomes clear that the two-state solution is definitively dead and that Israel's occupation of the West Bank will run forever, the chances of another Palestinian uprising, and wider unrest, will grow sharply.
Both Israel and the United States could find themselves at sharp odds with Sunni Arab partners in the region, such as Egypt, Saudi Arabia and Jordan. Israel likes to play up the improving ties it has with those countries, but that could quickly come to an end if it takes dramatic steps that sideline peace talks and kill any hope of a Palestinian state.