Public Security Minister Gilad Erdan said Israel now had "an opportunity to create together with the administration the conditions for serious peace negotiations by changing the basic approach of the international community".
"Until today the Palestinians had every reason to believe that time was on their side," said Erdan, a member of Prime Minister Benjamin Netanyahu's Likud party, speaking in Jerusalem at the Conference of Presidents of Major American Jewish Organisations.
"They could refuse to negotiate, incite terror, and attack Israel in the international arena, while the world put pressure only on Israel. This approach has failed."
Members of Netanyahu's rightwing coalition had hailed Trump's election as the beginning of a new era in which they would be able to freely advance settlement construction, considered by the international community as a major impediment to a Palestinian state and peace agreement.
But at his first meeting with Netanyahu last week since taking office, Trump on Wednesday asked the Israeli leader to "hold back on settlements for a little bit".
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And on Sunday, Netanyahu said the US and Israel had agreed to create teams on West Bank settlement, "an area that we have not previously agreed on".
Education Minister Naftali Bennett, who heads the far-right Jewish Home and opposes a Palestinian state, told the conference he was "happy that President Trump and Prime Minister Netanyahu are willing to explore new ideas".
That was a reference to Trump's comments that Washington would no longer insist on a two-state solution to the conflict.
The US ambassador to the United Nations, however, later disputed the notion that the US does not support the two-state solution.
According to Bennett, "it’s been 24 years of the same thing", referring to the period since the 1993 Oslo talks that were to have led to the formation of a Palestinian state.
The administration of previous US president Barack Obama strongly opposed the expansion of Jewish settlements, arguing they hurt the longer-term search for a two-state solution.
Since Trump's January 20 inauguration, the Israeli premier has announced more than 5,000 settlement homes and the construction of the first entirely new settlement for more than 20 years.