In a 20-minute meeting with Mohammed bin Salman at the G20 summit in Japan, described by officials as “serious”, Ms May also called for a”open and transparent” legal process in relation to the murder of journalist Jamal Khashoggi.
And officials said that she also spoke with the Prince about the need for de-escalation of tensions in the Persian Gulf, which has recently seen attacks on oil tankers in the Straits of Hormuz, and the preservation of the international deal preventing Iran from developing a military nuclear capability.
The de facto Saudi ruler - known as MBS - has become the focus of international condemnation since taking the helm in Riyadh in 2017, due to his bombing of neighbouring Yemen and alleged links to the Khashoggi killing.
Four years of the Saudi-led bombing campaign designed to oust the Houthi rebels who hold much of Yemen have led to more than 8,000 civilian deaths and 9,500 injuries, according to independent monitoring group Yemen Data Project. Britain last week froze arms sales to the Kingdom after a court ruled them unlawful because of the clear risk they could breach humanitarian law in Yemen.
A United Nations-led peace process has been threatened by allegations from the Saudi-backed official Yemeni government that envoy Martin Griffiths was siding with the rebels.
Meanwhile, a trial of 11 individuals at the Riyadh Criminal Court in relation to the Khashoggi murder has been taking place behind closed doors and the defendants - five of them facing the death penalty - have not been named.
A UN report found there was “credible evidence” that MBS and senior officials were individually liable for Khashoggi’s death at the Saudi consulate in Istanbul last October. But Riyadh insists it was the result of a “rogue operation” by agents who were intended to return him to Saudi Arabia.
Speaking after the meeting in Osaka, a senior British official said: “The prime minister reiterated the need to keep working on finding a solution to the current conflict in Yemen, which is causing significant humanitarian suffering, and the importance of continuing to make progress through the UN peace process.
“On accountability for the murder of Jamal Khashoggi, the prime minister said the legal process needed to be open and transparent.”
He added: “She underlined the need for urgent de-escalation of the current tension in the Gulf and the importance of preserving the JCPOA (Joint Comprehensive Plan of Action with Iran).”
Speaking ahead of the meeting, Ms May defended her decision to sit down with world leaders like MBS and Turkish president Recep Tayyip Erdogan, who has faced criticism for a heavy-handed response to the 2016 attempted coup in his country.
"These are all individuals sitting around the G20 table,” she said. “The G20 is about that international co-operation.
“I will be promoting that international rules-based order, I will be promoting that international co-operation and I will be giving that message to those that I meet individually and collectively around the G20 table.”
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