Dina el-Mamoun, the aid group's head of policy and advocacy in Yemen's capital, Sanaa, said the UN's Stockholm Agreement agreed last month between Houthi groups and the Saudi-backed government was "too vague".
"There is an issue with the actual agreement, which is actually quite vague," Mamoun told Al Jazeera.
"The UN should have made clear these basic issues that go to the heart of the agreement: who needs to hand over what and to whom."
Under the terms of the UN-brokered deal, the Houthis were expected to hand over control of the ports of Hodeidah, Saleef and Ras Isa, to "local security forces in accordance with Yemeni law".
Vague agreement
However, both sides have disagreed over the meaning of the text. The government says it means the ports should be handed over to the officials who ran the facility before the Houthis seized Hodeidah city in late 2014.
The Houthis, meanwhile, insist the deal refers to the officials currently running the port, who are their allies.
"How can the UN expect a vague agreement to translate, in reality, to what is intended without making it clear?" asked Mamoun.
"An agreement that leads us to a state of confusion over what was agreed is not what we needed."
The UN special envoy for Yemen, Martin Griffiths, met Houthi groups and members of his monitoring team in the country over the weekend before heading for Saudi Arabia to ensure the peace deal is fully implemented.
Skirmishes continue in and around the Red Sea port city despite the looming 21-day redeployment deadline imposed under a UN Security Council resolution, which set a withdrawal target of Tuesday.
UN spokesman Farhan Haq did not directly answer Oxfam's criticism, but said rebel and government leaders did not agree despite a "collective recognition of the urgency" of ending hostilities.
"Despite both parties consenting to the Stockholm Agreement, there is still a lack of common interpretation of the implementation and sequencing of the Hodaidah agreement," Haq told Al Jazeera.
"This is of course driven by the lack of trust among the parties and their apprehension with respect to making operational concessions, outside of a comprehensive political solution to the conflict in Yemen."
Haq urged both sides to respect the ceasefire and redeploy their forces in accordance with the deal.
"Anything short of that goal could derail the fragile progress being made to address the situation in Hodaidah," he added.