Angus Robertson, the SNP's leader at Westminster, has requested a meeting with David Cameron to discuss the ongoing crisis in Yemen.
He has urged the prime minister to halt arms sales to Saudi Arabia claiming the weapons are being used in its military campaign in the neighbouring country.
Mr Robertson said the situation meant the UK was "effectively at war".
The UK government said UK military personnel were not directly involved in operations by the Saudi-led coalition.
Air strikes and fighting on the ground in Yemen have killed 5,800 people, about half of them civilians, since a Saudi-led coalition began a military campaign to restore the internationally-recognised government last March, according to the UN.
The coalition comprises five Gulf Arab states and Jordan, Egypt, Morocco and Sudan.
Mr Robertson raised the situation in Yemen during Prime Minister's Questions on Wednesday.
He has now asked for a meeting with Mr Cameron and has highlighted a report commissioned by Amnesty International which claimed Britain was "breaking national, EU and international law by supplying weapons used by Saudi Arabia in a bombing campaign in Yemen".
The SNP said since May 2010, the UK government had overseen more than £5.6bn worth of military licences to Saudi Arabia including fighter jets, tear gas military vehicles and targeting equipment.
Mr Robertson said: "David Cameron needs to provide a full and frank disclosure of the UK's relationship with Saudi Arabia, and the UK's involvement in the war in Yemen - the lack of transparency has been alarming.
"World attention on conflict in Middle East is focussed on Syria and Iraq and sadly the catastrophic war in Yemen is largely overlooked, although it is claiming many lives and causing millions of people to flee their homes and become refugees.
"I have requested a meeting with the prime minister to raise the evidence which has recently come to light, and I will urge for the Commons Committee on Arms Exports Controls to be re-instated immediately to provide a level of scrutiny."
'Not directly involved'
The UK government said it operated "one of the most rigorous and transparent arms export control regimes in the world".
A spokeswoman added: "No licence is issued if it does not meet these requirements.
"We regularly raise with Saudi Arabian-led coalition and the Houthi the need to comply with International Humanitarian Law in Yemen.
"UK military personnel are not directly involved in Saudi-led Coalition operations, we are offering Saudi Arabia advice and training on best practice targeting techniques to help ensure continued compliance with International Humanitarian Law."
In response to Mr Roberston's comments at PMQs, Mr Cameron said the UK was "not involved in the Saudi targeting decision making process".