"We know that things are hard and complicated، but there is nothing impossible with good efforts،" he added.
The Palestinian administration had reportedly expressed pessimism at USA peace efforts, and Abbas had reportedly sought a US commitment to endorse the two-state solution.
President Trump's son-in-law and senior adviser Jared Kushner led last week's mission, with the delegation also including Jason Greenblatt, envoy for worldwide negotiations, and deputy national security adviser Dina Powell.
The U.S., however, has described the trip as productive.
However, the White House is yet to lay out a framework for negotiations following multiple meetings with Israeli and Palestinian leaders.
But Palestinian leaders note that the White House has not even said clearly whether its focus will be a two-state solution to the conflict, which has been longstanding USA policy.
News about the outcomes of the meeting between President Mahmoud Abbas and the United States delegation hit the front pages of the three Palestinian Arabic dailies on Sunday.
Abbas Presses for Two-State Solution, Kushner Provides No Clarity
Kushner met with PA chairman Mahmoud Abbas on Thursday، who said he highly appreciated Trump's peace efforts. Also, the team will examine economic steps ahead of a potential peace deal.
The US team is attempting to find a way to kick-start the Israeli-Palestinian peace process in hopes of reaching what Trump has called the "ultimate deal". "We didn't agree to this at all", said Aloul.
Most notably in a meeting with leftist Israeli lawmakers last week, Abbas noted that he'd met Trump's envoys "about 20 times" but they had failed to convey a commitment to a two-state solution to Israeli Prime Minister Benjamin Netanyahu, according to leaked comments. "We've also told the Americans that we want clarity on their approach".
US officials have said that they have not ruled out a two-state solution but that it is up to the two sides, not them, to agree on a way forward.
He said it was an option under consideration because "the American administration has not presented any initiative until now, while the Israelis continue with their settlement activities and refuse to abide by obligations they signed up to".
"Without a vision it will be negotiations for negotiations sake،" he opined.
"I believe (Trump's) leverage has declined considerably, at least from the point-of-view of getting major concessions or a commitment to a major programme toward two states from the leaders, so that's why I think the shift should come to the more practical on-the-ground steps", he said.