The Houthi-run Saba news agency reported on Saturday that the memorandum, signed between Foreign Minister Hisham Sharaf Abdullah and the UN Humanitarian Coordinator in Yemen, Lise Grande, would include transporting critically ill Yemenis abroad from Tuesday 18 September, for a period of six months.
"The memorandum of understanding is the first step to alleviate the suffering of patients in need of treatment abroad," said Abdullah.
"The move does not in any way mean we are delaying our demand to reopen Sanaa International Airport for commercial and civil flights. The air bridge covers only a limited number of cases, but it is necessary in light of the continued siege and aggression."
Fighting has intensified in the war-ravaged country after UN-sponsored peace talks collapsed before they could officially start.
The talks, which would have been the first in nearly two years, were scheduled to take place in the Swiss city of Geneva on September 6 but the Houthi delegation failed to leave Sanaa.
Al Jazeera's Andrew Simmons, reporting from neighbouring Djibouti, said Saturday's agreement could mark a "potential breakthrough" following the failure of the summit.
"The Houthis have been in the Omani capital meeting with UN officials, including Martin Griffiths, the UN special envoy. They say they have signed a memorandum of understanding to transport a number of injured people abroad."
However, a source told Al Jazeera that it was unclear how many Yemeni patients would be affected by the decision, whether the agreement would include wounded fighters, and where they would be transported to.
There was also no immediate reaction from the UN.
'Lives hang in the balance'
The humanitarian crisis in Yemen has worsened "dramatically" since UN-sponsored peace talks collapsed and fighting resumed in the port city of Hodeidah.
Grande said on Thursday that "hundreds of thousands of lives hang in the balance" in the rebel-held city, where "families are absolutely terrified by the bombardment, shelling and air strikes".
She warned that fighting in Hodeidah, the entry point for the bulk of Yemen's commercial imports and aid supplies, could trigger famine in the impoverished nation where an estimated 8.4 million people are facing starvation.
The three-year war has unleashed the world's most urgent humanitarian crisis in the nation of 28 million people, with 22 million dependent on aid.
"We're particularly worried about the Red Sea mill, which currently has 45,000 metric tonnes of food inside, enough to feed 3.5 million people for a month. If the mills are damaged or disrupted, the human cost will be incalculable," Grande said in a statement.
Yemeni forces, backed by a Saudi and United Arab Emirates military alliance, said earlier this week that they had seized the main road linking the port city of Hodeidah to the capital, Sanaa, blocking a key supply route for the Houthi rebels who control much of the country's north.
More than 120,000 civilians have fled their homes since June 13 to escape the fighting, and on Saturday, smoke could be seen rising from parts of the city.
Martin Griffiths, the UN special envoy on Yemen, is expected to meet Houthi representatives as well as Yemeni government officials living in exile in Saudi Arabia this week in a bid to revive talks.
According to the UN, at least 10,000 people have been killed since the Saudi-Emirati-led coalition intervened in Yemen in 2015.
The death toll, however, has not been updated in years and is likely to be much higher.