The visit of Mohammed bin Salman, whose powers include his role as defense minister, comes amid a diplomatic row with the United Nations and policy differences with the United States over the war in Syria and relations with Iran.
Prince Mohammed, spearheading an ambitious plan to revamp the economy of the world's top oil exporter, will also travel to California where he is expected to meet company executives in Silicon Valley, the Saudi-owned Asharq al-Awsat newspaper said.
The royal court said in a statement late on Sunday that the prince would discuss ways of strengthening relations with the United States, which have cooled under Obama's presidency.
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Saudi Arabia, a leading supporter of Syrian rebels fighting to oust President Bashar al-Assad, has been critical of what it sees as foot-dragging by Washington over efforts to end the conflict.
It has also urged Obama to take a tougher stand on what Riyadh sees as Iranian meddling in the affairs of Arab states. Iran denies such interference.
Asharq al-Awsat quoted Saudi sources as saying that Prince Mohammed, a son of King Salman, would start his visit in New York where he was expected to meet the UN chief on Monday.
Ban said last week that Saudi Arabia had exerted "unacceptable" pressure on the world body after a UN report blacklisted a Saudi-led military coalition for killing children in Yemen, a charge denied by the kingdom.
The United Nations removed the coalition from the list after Riyadh threatened to cut its funding of UN programmes, diplomatic sources said.
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The prince would then meet Obama as well as Secretary of State John Kerry and Defense Secretary Ash Carter in Washington, the newspaper said.
State news agency SPA said that a number of senior officials, including Finance Minister Ibrahim Alassaf and Commerce and Investment Minister Majid al-Qusaibi were part of a delegation accompanying Prince Mohammed, but it did not specify who he would meet during the three-day visit.
Under broad economic reforms announced last week, which aim to free Saudi Arabia of its dependence on oil exports, the kingdom is seeking a big increase in foreign investment and tie-ups with foreign companies in non-oil industries including the technology sector.
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