The monarch greeted Mohammed bin Salman at Buckingham Palace as he began a controversial trip to the UK, which is expected to be met by protests.
As the royals met, Labour leader Jeremy Corbyn prompted a political row by claiming “British military advisers are directing the war” in Yemen.
A Saudi-led coalition has been conducting military operations there in an attempt to reinstate Yemen’s official government after much of the country was seized by Houthi rebels.
The conflict has attracted accusations of breaches of international law amid civilian casualties.
Quizzing Theresa May about the UK-Saudi relationship at Prime Minister’s Questions on Wednesday, Mr Corbyn added: “It cannot be right that her Government is colluding in what the United Nations says is evidence of war crimes.
“Will the Prime Minister use her meeting today with the Crown Prince to halt the arms supplies and demand an immediate ceasefire in Yemen?”
The Labour leader’s comments brought an immediate rebuttal, with Middle East minister Alistair Burt declaring Mr Corbyn’s claim was “just not true”.
“I perhaps know more about what our officers are doing than the Leader of the Opposition,” he told the BBC.
“It’s not true they are directing the war in Yemen. They’ve given advice in relation to how targeting is done, to make sure civilians are not involved.
“But, to say they’re involved in the conduct of the war is simply untrue.”
International Development Secretary Penny Mordaunt, a former armed forces minister, insisted the UK’s armed forces “go to great lengths and often put themselves in greater danger” to uphold international humanitarian law.
Responding to Mr Corbyn in the House of Commons, the Prime Minister told the Labour leader she was “concerned about the appalling humanitarian situation in Yemen”.
She highlighted how more than £200m in aid made the UK the third largest humanitarian donor in Yemen.
Mrs May added: “I was pleased when I went to Saudi Arabia in December, I met with the Crown Prince, I raised with him them the need to open the port of Hodeidah to humanitarian and commercial supplies.
“I’m pleased to say Saudi Arabia then did just that. This vindicates the engagement that we have with Saudi Arabia, to be able to sit down with them.
“Their involvement in Yemen came at the request of the legitimate government of the Yemen. It is backed by the United Nations Security Council and, as such, we support it.”
The Prime Minister stressed it is “for all parties in the conflict” to ensure humanitarian aid is able to get to those in need.
Mr Corbyn highlighted millions facing starvation in Saudi Arabia’s southwestern neighbour, and 600,000 children suffering from cholera.
Earlier, the Labour leader urged the Prime Minister to call on the Crown Prince to halt “the shocking abuse of human rights in Saudi Arabia” during her meeting with him.
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In response, Mrs May claimed the UK’s “historic” link with Saudi Arabia “has saved the lives of potentially hundreds of people in this country” and confirmed she would be raising human rights concerns with the Crown Prince.
At the beginning of their exchanges, the Prime Minister had accused the Labour leader of “mansplaining” after he noted how Thursday is International Women’s Day.