"The US administration of President Donald Trump is seriously considering a solution to the Palestinian issue," Abbas told AFP yesterday after a meeting of the Arab League in Jordan.
Abbas met with Trump's Middle East envoy Jason Greenblatt before leaving for the summit and said contacts with the administration were ongoing.
"(There is) continuing dialogue with the American administration and there were a number of issues they wanted our opinion on or our answer to them," he added.
Abbas is expected to meet with Trump in Washington for the first time in April.
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Trump is also expected to meet other Arab leaders in the coming weeks, including Egyptian President Abdel Fattah al-Sisi and Jordan's King Abdullah II.
Trump caused alarm among Palestinians and many parts of the international community in February when he broke with years of US policy in support of the two-state solution, meaning an independent Palestinian state alongside Israel.
"I'm looking at two-state and one-state, and I like the one that both parties like," Trump said at the White House before a meeting with Israeli Prime Minister Benjamin Netanyahu.
In their final statement, the leaders called for a revival of "serious and productive peace negotiations between Israelis and Palestinians" and renewed their commitment to a two-state solution.