The U.N. -brokered agreement is aimed at alleviating the world's worst humanitarian crisis.
Houthi rebels in Yemen say they have begun a withdrawal from three key strategic ports that serve as a vital lifeline for food and humanitarian aid into the war-torn country.
It is the first major step in implementing the deal, which was reached by the Saudi-backed Yemen government of President Abed-Rabbu Mansour Hadi and the Iran-aligned Houthis for a ceasefire and troop withdrawal in Hodeidah a year ago.
"The government rejects any unilateral withdrawal of the rebel forces from Hodeidah without allowing for a joint monitoring and verification of implementing the Stockholm Agreement", said Iryani. The UN deal was meant to stop Saudi-led forces from destroying the ports, and involves the Houthis leaving the ports to local forces.
The rebel withdrawal is part of a ceasefire agreement that requires all forces to pull out of Hodeidah and for the ports to be placed under United Nations supervision.
Yemen's Saudi-backed government warned that the Houthis might attempt to mislead the global community before the next U.N. Security Council consultations on Yemen on Wednesday...
Yemeni coast guard officer shakes hands with members of the Houthi movement during withdrawal from Saleef port in Hodeidah province, Yemen May 11, 2019.
Sources close to the Iran-aligned Houthis told media that the ports were handed over to coast guard personnel who were in charge before the rebels took over nearly five years ago.
Video footage obtained by the BBC on Monday - the first day - shows Houthi forces setting off in trucks.
The U.N.'s Redeployment Coordination Committee (RCC) has said that the Houthis would make an "initial unilateral redeployment" between May 11 and May 14 from Saleef, Ras Isa and Yemen's main port of Hodeidah.
There was no independent confirmation of a rebel withdrawal, and a United Nations observer mission in the city of Hodeida remained cautious in its initial assessment.
The conflict in Yemen has already claimed tens of thousands of lives and put millions on the brink of starvation in what was already the poorest country on the Arabian Peninsula.
Sources saw this as a sign United Nations envoy Martin Griffiths had managed to get the warring sides to agree to the plan, since the coalition had quickly rejected a previous attempt by the Houthis to unilaterally withdraw last December.
Hodeidah has become the focus of the war since a year ago when the coalition twice tried to seize its port to cut off the Houthis' main supply line.
In the second phase, both sides would pull troops 18 km outside the city and heavy weapons 30 km away.
The military coalition led by Riyadh intervened in March 2015 when President Abedrabbo Mansour Hadi fled into exile in Saudi Arabia after the rebels captured swathes of the country.