The United Nations submitted a proposal to the legitimate Yemeni government and Iran-backed Houthi militias on lifting the militias' siege on the Taiz province.
Delegations from the government and Houthis have been holding a second round of negotiations on ending the siege in the Jordanian capital, Amman.
The government appealed on Tuesday to the international community, European Union ambassadors and United States' envoy to Yemen to exert more pressure on the Houthis to reopen the main routes leading to Taiz.
The Houthis have been resisting this demand, suggesting instead the opening of dirt roads, in what was seen as an attempt to thwart UN efforts to end the siege.
The UN proposal calls for opening five roads, including the main route, leading to the province.
The government delegation stated that after two weeks of talks, the Houthis continue to insist on opening dirt roads that do not help in easing the siege or the suffering of the people.
The government has been committed to the UN proposal on opening the main roads, it added, accusing the Houthis of acting unilaterally "to impose a fait accompli that no one has agreed to" and forcing the negotiations to come to a halt.
It hailed UN envoy Hans Grundberg and his team's efforts in the negotiations, hoping they would exert greater pressure on the militias and prevent them from stalling and undermining the nationwide truce.
Ending the siege on Taiz is among the main points of the UN truce, which was extended for another two months last week.
Grundberg issued a statement on Monday to sum up the Amman negotiations, saying he had submitted a "revised proposal on the phased reopening of roads, including an implementation mechanism and guarantees for the safety of civilian travelers, based on the discussions with both sides."
"The updated proposal calls for the reopening of roads, including a main route, leading into and out of Taiz city, as well as roads in other governorates that aims to alleviate civilian suffering and enhance the delivery of goods."
"The proposal takes into consideration suggestions from both parties, as well as feedback from Yemeni civil society. It also takes into account concerns expressed by the parties," read the statement.
"This is a first step in our collective efforts to lift restrictions on the freedom of movement of Yemeni women, men and children within the country."
"The parties have a moral and political responsibility to engage seriously and urgently with the UN proposal, prioritizing the interests of civilians and delivering immediate and tangible results to the people of Taiz and Yemen at large," Grundberg said.
"While I continue my efforts and engagement with the parties on this file, I hope the proposed initiative will sustain the momentum needed to move towards discussions on more durable arrangements within the multi-track process."