The leader of the Houthi movement in Yemen has condemned the British foreign secretary for pressing Germany to relax its arms sales ban on Saudi Arabia, saying it was not possible for the UK to be a peace-broker in the country and an arms seller.

“Britain sending aid does not change the tragic reality of its arms sales. Jeremy Hunt cannot promote peace while at the same time acting as an arms salesman,” said Mohamed Ali al-Houthi, the head of the supreme revolutionary committee, in an interview with the Guardian.

His comments are the most direct criticism yet of Hunt, who has been acting as a mediator in the four-year civil war in Yemen.

Germany announced in November that due to the killing of the dissident journalist Jamal Khashoggi by Saudi agents it would provide no further arms export licences to Saudi Arabia. It has not formally banned previously approved deals but has urged industry to refrain from such shipments for now.

Sunday was the deadline for the ban to end unless an extension was agreed, which resulted in a compromise this week whereby the ban was extended for another six months , but with a loophole inserted that gives German defence firms until the end of the year to complete contracts that supply parts for UK and France arms sales.

The German government said efforts would be made to ensure that these jointly supplied arms were not used in the war in Yemen, although how such a condition can be enforced is unclear. A half-complete bilateral German contract for 35 patrol boats may also be allowed to go ahead, but not sent to Saudi Arabia.

Britain has been worried about the sale of 48 Eurofighter jets to Saudi Arabia, and needs parts from Germany. Britain says its arms sales are lawful since the weapons are not at risk of being used in breach of international humanitarian law.

Both Hunt and the French government have been lobbying the German coalition to allow the arms sales, but there has been an impasse between the Social Democrats, who oppose the sales, the Christian Democrats, who back them.

The resolution of the German dispute is seen by the European arms industry as critical to ensuring Europe has an integrated defence policy.

The UK has sold at least £5.7bn worth of arms to the Saudi-led coalition fighting in Yemen since 2015, according to a Sky News analysis of figures published on Friday.

Condemning the UK role, Houthi added: “Mr Hunt has gone beyond defending British arms sales, by attempting to pressure other European countries, such as Germany, to sell arms.

“If it wasn’t for the joint British, US, Saudi, and UAE naval forces, the existing famine and the tragic humanitarian situation wouldn’t reach such critical levels, including as he admits about 24 million Yemeni need an emergency aid of food and medicine.”

Houthi said: “The Saudi-led coalition, backed by Britain, commits war crimes and does not abide by, as Britain claims, ‘the most stringent guidelines for the export of weapons in the world’. The principles mentioned are solely for political speech and to avoid the legal and moral responsibility concerning the war crimes and humanitarian situation that the British government faces as part of such alliance”.

France has also demanded that the arms sales ban be relaxed. France’s ambassador to Germany, Anne-Marie Descôtes, said in an open letter this week that the German arms export policy and cumbersome licensing rules threatened future bilateral defence projects.

Tuesday marked the fourth anniversary of the intervention by a western-backed military coalition led by Saudi Arabia in Yemen’s civil war, which has killed at least 60,000 people, left half the country’s 22 million population food insecure and sparked the worst cholera outbreak in modern history.

The coalition and the western governments who supply it with arms have been repeatedly criticised by rights groups and conflict monitors for bombing campaigns which have hit schools, health facilities, funeral gatherings and wedding parties, killing thousands of civilians. Yemen’s government and Saudi Arabia accuse the Houthis of using civilians as human shields. The Houthis have launched long-range missiles into neighbouring Saudi Arabia and targeted Saudi ships in the Red Sea. All side may be responsible for war crimes, the UN has said.

The UN special envoy for Yemen, Martin Griffiths, was in Riyadh this week to discuss the stalled peace effort in Yemen, including the question of the Saudi-backed and UN-recognised government of Yemen accepting a new security force in the Red Sea port of Hodeida. Diplomats fear that neither side have sufficient incentive to compromise.

The Houthi criticism will have riled the foreign secretary, who would argue that he has gone further than his predecessors in using his private influence on the Saudis to urge them to show restraint and patience in the face of delays in implementing a peace agreement set out in Stockholm in December.