Their comments came ahead of talks today with Trump aides, including special representative for international negotiations Jason Greenblatt and the president's son-in-law and Middle East envoy Jared Kushner.
The visit for meetings with both Israeli and Palestinian leaders comes with many analysts expressing little hope that major progress can be made on Israeli-Palestinian peace for now.
Trump's aides have been ferrying between leaders from the two sides in recent months in attempts to restart direct talks, with the aim of achieving what the US president has called the "ultimate deal".
But Palestinian officials have become increasingly frustrated with the administration and pessimistic about chances of a breakthrough.
President Mahmud Abbas reportedly told Israeli leftwing politicians recently that despite more than 20 meetings with US officials he was still unclear what Trump's strategy was.
Ahmed Majdalani, a senior member of the Palestine Liberation Organisation which Abbas heads, told AFP they were demanding "a clear and frank answer on the position of the administration on the two-state solution and settlements".
"Without a clear American commitment to the two-state solution and stopping settlements and ending the occupation, we don't expect much from this administration."
The president acknowledges that "there are likely to be a lot of ups and downs on the way to peace and making a peace deal will take time", but he "remains optimistic that progress toward a deal can be achieved", he said.
Kushner and other US officials met on Tuesday evening with Jordan's King Abdullah II.
Previous US governments have committed to an independent Palestinian state alongside Israel, but Trump broke with longstanding US policy in February by saying he would be happy with either a one-state or two-state solution if the parties were happy.
The administration has also sought to protect Israel at the United Nations from criticism of its occupation of Palestinian land.
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