Speaking before entering talks with Israeli Prime Minister Benjamin Netanyahu in New York, Trump said that it was a "dream" of his to bring about a peaceful solution to a conflict that has eluded several of his predecessors.
"I would say over the next two to three to four months," Trump said, referring to his prospective timetable for presenting a plan as he met Netanyahu on the sidelines of the UN General Assembly.
Trump for the first time said explicitly that he backed a two-state solution that would create an independent Palestine, saying: "That's what I think works best, that's my feeling."
Palestinian official says US will never present Middle East peace plan
"I really believe something will happen. It is a dream of mine to be able to get that done prior to the end of my first term," added Trump, who was elected to a four-year term through January 2021.
The Middle East peace process has effectively been stalled since the Palestinians broke off contacts with the Trump administration last year in protest at the US president's decision to recognize Jerusalem as the capital of the Jewish state.
The Palestinians also want Jerusalem to be their capital and have long argued that the status of the holy city should only be settled as part of a larger peace agreement.
Trump cites Middle East progress, but mum on peace plan
Relations between the Palestinian Authority and the United States have fallen even lower in recent weeks after Washington cut off funding, including to a UN agency that helps millions of Palestinian refugees.
Trump, however, said that he was in no doubt that the Palestinians would soon return to the negotiating table.
"They are absolutely coming back to the table," he said. "Absolutely, 100 per cent."
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