The G20 summit in Argentina is the first major international event Prince Mohammed has attended since the murder of the Washington Post columnist, a critic of the crown prince, in the Saudi consulate in Istanbul in October.
"The Prime Minister stressed the importance of ensuring that those responsible for the appalling murder of Jamal Khashoggi are held to account, and that Saudi Arabia takes action to build confidence that such a deplorable incident could not happen again," May's office said in a readout of her meeting with Prince Mohammed.
May had earlier pledged to be robust when she talked to bin Salman and said that the investigation into Khashoggi's killing must be full and credible.
May is keen not to alienate allies around the world as Britain prepares to leave the European Union next year in its biggest foreign and trade policy shift in more than 40 years.
French President Emmanuel Macron told the crown prince earlier on Friday that Europe would insist on international experts being part of the investigation into the murder of Khashoggi.
May will also meet with Turkish President Tayyip Erdogan on Saturday, a senior British official said, with discussion likely to include Turkey's investigation into the killing.
May also encouraged the Saudis to end the conflict in Yemen. Western nations are calling for an end to the Saudi-led military campaign, launched by Prince Mohammed, as a humanitarian crisis there worsens.
"On Yemen the Prime Minister set out the urgent need to bring an end to the conflict and bring relief to millions threatened by famine," she said. She urged Saudi support for United Nations Special Envoy Martin Griffiths and for progress at the upcoming Stockholm talks.
Britain has come under pressure to cease arms sales to Saudi Arabia because of the high death toll in air raids by the Western-backed Saudi-led coalition in Yemen. (Reporting by Kylie MacLellan, writing by Sarah Young and Caroline Stauffer; editing by Guy Faulconbridge, Hugh Lawson and Tom Brown)
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