The outcome of the investigation into the murder of the Washington Post columnist Jamal Khashoggi could potentially impact on British support for Saudi Arabia’s involvement in the war in Yemen, the UK’s Middle East minister has said.

Speaking on Tuesday, Alistair Burt told the House of Commons it was “not an illegitimate question” to ask whether the inquiry would reveal something of the character of the regime in Riyadh and that this would have a bearing on the war in Yemen, which Saudi Arabia entered in 2015.

In an often stormy session of the international development select committee, Burt stood his ground despite warnings from aid agencies that Yemen was heading towards one of the worst famines in history and claims he was not using British diplomatic influence at the UN to end the civil war between the Saudi-backed government and Houthi rebels.

He rejected impassioned calls by aid agencies and former senior diplomats for the UK to use its influence to demand a unilateral ceasefire and the full deployment of humanitarian aid.

A London meeting of the Elders, the most senior group of former UN diplomats, called for the UK to encourage the UN to take urgent, credible action to lift the humanitarian blockade. The group, chaired by the former UN climate change special envoy Gro Harlem Brundtland, also demanded an end to arms sales to Saudi Arabia.

Burt was speaking as the UK foreign secretary, Jeremy Hunt, held unscheduled talks in London with Martin Griffiths, the UN special envoy for Yemen. Conservative backing for the war in Yemen has been badly damaged by the Khashoggi murder, even if there is little support for the Iranian-backed Houthis.

Burt repeatedly insisted the UK was not a party to the conflict and blamed the Houthis for the failure of talks organised by the UN envoy in Geneva.

His claim drew a furious response from the Labour MP Lloyd Russell-Moyle, who told Burt: “We arm the Saudis. We maintain the air force. We have British soldiers embedded in the control centres. We command the war flight paths. We train Saudi pilots in Wales – the only thing we don’t do is press the button to drop the bomb.

“Can we just not be honest? We are party to this war. We have decided to cosy up to a regime that dismembers its own civilians in consulates of Nato allies.”

Burt responded, saying: “We are not party to the conflict, we do not control any flight paths, the coalition is acting in defence of a legitimate government.”

Ending UK support for Saudi Arabia would not bring an end to the conflict, he added, while rejecting efforts to push for a new ceasefire resolution at the UN, saying Griffiths did not support such a move since it was unlikely to be accepted on the ground.

Earlier, Jan Egeland, the secretary general of the Norwegian Refugee Council, said the UK was one of a small group of countries that could stop Yemen’s relentless deterioration.