The UN spokesman Farhan Haq confirmed to reporters at the UN headquarters in NY on Saturday that the Houthi rebels' withdrawal from Hodeidah ports "has begun".
"The UN has started monitoring this unilateral step", a source told reporters. The UN monitors plan to report to the Security Council about the situation on May 15.
The council is due to hear a briefing on Hodeidah on Wednesday.
Yemeni warring parties reached a peace deal on Hodeidah in December previous year as the first step toward a comprehensive political solution.
Government officials have questioned whether the Houthis are actually withdrawing from the ports or simply handing over to control rebel fighters in disguise.
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"They took this fake step to avoid being identified as the party responsible for hindering the peace process in Yemen", Mr Al Qudaimi said.
Some officials from the Saudi-backed, internationally recognized Yemeni government dismissed the pullout as a "show", but government negotiator Sadiq Dweid acknowledged it marked the start of implementing the Stockholm accord.
"What happened today is a flagrant show, a group of (Houthi) militiamen left (the city) and they were replaced by others wearing coast guard police uniforms", Information Minister Muammar Al-Iryani told Reuters.
Yemeni Information Moammar Al Eryani on Saturday described the operation as an attempt to mislead the worldwide community, which has been increasing pressure for an end to the war. The U.N. -brokered agreement is aimed at alleviating the world's worst humanitarian crisis.
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.
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Both the Houthis and government forces agreed to withdraw from Hudaydah to allow in vital humanitarian aid.
A United Nations source told Reuters on Saturday that the RCC would announce its assessment of the Houthi redeployment next week.
The government forces, backed by the Saudi-led coalition, have advanced to the southern outskirts of the port city since June 2017, but the forces have halted a major offensive to recapture Hodeidah to pave the way for peace efforts.
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.
The port of Hodeida is one of Yemen's most important lifelines.
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The conflict in Yemen, which saw a Saudi Arabian-led coalition launch a prolonged bombing offensive against the country's Houthi rebel movement, has created what the United Nations deems the worst humanitarian disaster in the world, marked by tens of thousands of deaths and millions more facing starvation.