Every day the war in Yemen goes on “is a day that a mother loses their child”, the UN’s envoy to the country has said as he announced a plan to restart peace talks.

The scheme would introduce a set of confidence-building measures within a week, including reopening Sana’a airport, prisoner swaps and payment of civil service salaries.

It was arranged by the UN special envoy Martin Griffiths after a frenetic round of meetings in New York designed to prevent Yemen from sliding towards a humanitarian disaster as fighting escalates.

Griffiths said he was optimistic that overlapping steps could be agreed by Houthi rebels and a Saudi-led coalition that includes the United Arab Emirates and that backs the UN-recognised government of Yemen.

He said: “There is a huge appetite for this. Both sides reconfirmed to me their desire to be reconvened, and they both recognise that there is no other solution to this war apart from through this process. We are now working on ways to get them back together as soon as possible.”

He said as many as 5,000 prisoners on either side needed to be exchanged. Sana’a airport is blocked by the Saudis.

Griffiths said the confidence-building measures had been due to be discussed at talks in Geneva a fortnight ago that did not in the end take place. He said there was no need for the two sides to be in the same building for the measures to be agreed.

The talks in Geneva would have been the first between the two sides for two years, but the Houthis refused to travel from Yemen after seeking assurances about the safe passage of some of its wounded soldiers.

Griffiths admitted he had no power to demand a ceasefire or prevent the Saudi coalition from pressing ahead with plans to capture the strategic Red Sea port of Hodeida, through which most humanitarian aid into the country flows.

“What I won’t do is to make stopping the war a condition for us to resolve it,” he said.

In the wake of the collapse of the Geneva talks, the UAE announced plans to restart the military action.

In a letter to the UN security council on 15 September, it said: “The Houthis would not have engaged with the special envoy unless there was a fear of losing access to the Red Sea along with the supply of weapons and funds that sustain them. The capture of Hodeida is critical to re-engaging the Houthis in peace talks.”

Aid agencies in New York urged the Gulf states not to press ahead with plans to besiege the city or to cut off the aid supply, including to the Houthi-held capital, Sana’a. The UK, which advises Saudi Arabia on military and political strategy, says it has been calling for restraint.

Sixty-day-old Nadia Ahmad Sabri, who suffers from severe malnutrition, lies in bed at a malnutrition treatment centre in the Red Sea port city of Hodeida, Yemen December 20, 2017. Photograph: Abduljabbar Zeyad/Reuters

In a sign of the complex diplomatic cross-currents over Yemen, EU states including the UK clashed with Saudi Arabia on Friday by backing a one-year extension of the mandate for an independent group of experts set up to investigate breaches of humanitarian law in Yemen.

In a report in August that was rejected by the Saudi-backed Yemeni government, the experts said they had found widespread breaches of the law and said the predominant responsibility for deaths lay with the Saudi coalition.

At a meeting of the UN Human Rights Council, the mandate to renew the experts’ work was passed by 21 votes to eight, with 18 abstentions. The Gulf states and China opposed the move, while the UK said the humanitarian situation and human rights in Yemen were deteriorating.

The UK said: “It is important to give the group of eminent experts more time to fully examine the conflict and to ensure that their conclusions accurately reflect the conduct of all parties in future reporting. It is clear that many incidents and alleged violations committed by all parties have not yet been fully documented, particularly those committed by Houthis.”

The UK foreign secretary, Jeremy Hunt, met the Saudi and UAE foreign ministers on Thursday, in part to discuss the humanitarian crisis and to stress the need for a political solution.

Speaking at the Council on Foreign Relations, the Saudi foreign minister, Adel al-Jubeir, said a fund set aside to rebuild Yemen would be doubled to $20bn due to the scale of the conflict.

He said Saudi Arabia had lost “the communications battle at the beginning of the war and that is why our reputation has taken a big hit”.