The British government does not expect Saudi Arabia to execute Ali al-Nimr, who was sentenced to death for taking part in an anti-government protest in 2012 at the age of 17.
Ali al-Nimr received a sentence of death by crucifixion, prompting international outcry.
But Foreign Office Minister Tobias Ellwood today told MPs he expects the sentence will not be carried out.
It was announced on Saturday that 47 alleged terrorists had been executed in the country, including leading Shia cleric Sheikh Nimr al-Nimr, a prominent critic of the Saudi authorities.
Ali al-Nimr is his nephew.
Mr Ellwood told the Commons in a statement: "The Saudi Arabian government is well aware of our views and we will continue to raise our concerns with them.
"We also raised the case of Ali al-Nimr with the Saudi authorities again over the weekend.
"We expect that Ali al-Nimr and the two others who were convicted as juveniles will not be executed."
Mr Ellwood spoke of the UK's "close relationship" with Saudi Arabia, but insisted that "does not mean that we shy away from raising legitimate human rights concerns".
He added: "We make this point very clearly in public and in private.
"The Saudi authorities are well aware of our views and I have raised them most recently myself with the Saudi authorities yesterday following the execution of 47 people over the weekend, 43 of which were Sunni."
Mr Ellwood said that escalating tension between Saudi Arabia and Iran is "deeply concerning" as he called for calm.
"I urge all parties in the region urgently to show restraint and responsibility and to work towards resolving tensions," he said.
Shadow foreign secretary Hilary Benn criticised the Government for not naming Sheikh al-Nimr when condemning the executions.
The Labour frontbencher described the Sheikh's execution as "profoundly wrong" and the cause of a major crisis in the Middle East, with several Sunni countries including Saudi Arabia severing diplomatic ties with Iran following protests and violence.
Mr Benn said: "In a region that is already in ferment, with the brutal civil wars in Syria and Yemen and the threat from Daesh not just in Syria and Iraq but also in Egypt, Libya and elsewhere, you must surely recognise that the execution of Sheikh Nimr al-Nimr and 46 other people has caused a major diplomatic and political crisis.
"And surely the basis of any close relationship has to be that the two parties are honest with each other.
"We too oppose the use of the death penalty in every circumstance including what has happened in Saudi Arabia.
"But on this side of the House we believe that the Saudi government was profoundly wrong to have executed Sheik al-Nimr, a Shia cleric, and three young Shia men whose alleged offences appear to have involved taking part in political protests and demonstrations against the current government.
"You will have noticed that neither the Prime Minister's comments or your statement today mentioned Sheikh Nimr al-Nimr by name. And I say that is a matter of great regret."
Mr Benn said the execution of Sheikh al-Nimr has implications for Syrian peace talks in Vienna and also Yemeni peace negotiations.
Replying, Mr Ellwood said Saudi Arabia had told Britain that it wanted to continue to participate in the Vienna talks and praised Iranian president Hassan Rouhani for condemning violence at the Saudi Arabian embassy in Tehran.
He said: "We need to de-escalate those tensions.
"We have had confirmation from Saudi Arabia that they want to continue to participate in the Vienna talks and I'm pleased to see the president of Iran actually condemn what has happened at the Saudi Arabian embassy and indeed at the consulate as well. To condemn those actions which is so important if we are to see a de-escalation of tensions."
MPs raised concerns over the export of weapons to Saudi Arabia.
Labour former minister Fiona Mactaggart told Mr Ellwood: "Isn't it time perhaps for the Saudi authorities to face concrete action from Britain like an end to arms exports, rather than continued expressions of concern?"
The minister replied: "I'm reminded about what Labour's policy was towards Saudi Arabia over the last 13 years.
"We have to have clear and precise rules on the export licensing schemes around the world. We simply cannot do it by whim or by choice about whether somebody is flavour of the month or not.
"There are rules we actually follow. Saudi Arabia has the right to defend itself, it has the right to purchase weapons systems as well.
"No country has the right to purchase weapons systems off us and then abuse them or use them incorrectly - then the licensing scheme kicks into process and makes sure those sales are revoked."
Liberal Democrat former minister Tom Brake asked Mr Ellwood if the UK Government would lobby to get Saudi Arabia to stand down as the chair of the United Nations Human Rights Council.
Mr Ellwood replied: "No, we won't."
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