"They got it from one side, from the other, and you know it would be great if we could make a peace deal with them," Trump said of Iran, a key backer of the Palestinian militant group Hamas, during a speech to Israel's parliament.
"Would you be happy with that? Wouldn't it be nice, I think. Because I think they want to."
Trump said the ball was in Tehran's court for any agreement to come to pass.
"We're ready when you are," the Republican said.
Trump also defended pulling Washington out of an agreement brokered under ex-president Barack Obama on Iran's nuclear programme, long a sticking point in Israel's relations with its arch-foe.
"I terminated the Iran nuclear deal and I was very proud to do it," Trump said.
"Yet even to Iran, whose regime has inflicted so much death on the Middle East, the hand of friendship and cooperation is open," he told the Knesset.
"They want to make a deal and we're going to see if we can do something," he added.
"Neither the United States nor Israel bear the people of Iran any hostility. We merely want to live in peace."
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