Israel regards the divided city as its capital but many countries, including its ally the United States, have resisted moving their missions there while its status and borders are still a matter of dispute.
Palestinians also see the city -- which is holy to Jews, Christians and Muslims -- as their future capital, and any final peace deal between the peoples would have to include an agreement on sovereignty.
Trump is the frontrunner for the Republican US presidential nomination, despite previously risking the wrath of conservative foreign policy voters by suggesting he would be neutral in the Israeli-Palestinian dispute.
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But on Monday, shortly before addressing the pro-Israel AIPAC lobby in Washington, he told CNN: "There's nobody more pro-Israel than I am. We have to protect Israel. Israel is so important to us."
And, asked whether he would recognize Jerusalem as Israel's capital and move the US embassy from Tel Aviv to Washington. Trump replied: "Yes, I would."
"The fact is I would like to see it moved, I would like to see it in Jerusalem," he said.
In 1967, with Israel under attack from Arab armies, Israeli forces occupied East Jerusalem, driving back Jordanian troops and taking control of some areas with majority Arab populations.
Palestinians still campaign for an Israeli withdrawal from the east of the city -- and Jordan still has administrative responsibility for the holy sites on the Temple Mount area of the Old City.