He said the monitors are expected to allow the entry of observers from the government team to verify the militias' pullout.
Yemen s government on Sunday accused rebels of a "policy of deception" after they announced a pullout from a string of Red Sea ports in a long-delayed move agreed under a ceasefire deal previous year.
"The Houthis are manipulating through choosing this unilateral announcement".
Under the first phase, the Houthis would pull back five km (three miles) from the three ports over the next four days.
Gen Lollesgaard chairs the committee of government and rebel representatives that is meant to oversee its implementation.
The spokesman for the Yemeni government's delegation to the RCC, Sadiq Dweid, said on Twitter that a Houthi withdrawal is "the first step of the first stage".
Houthis began the long-delayed withdrawal from three ports as part of a cease-fire deal reached in Sweden in December.
Hodeidah port is the main entry point for the bulk of Yemen's imports and humanitarian aid, serving as a lifeline to millions of civilians pushed to the brink of starvation by more than four years of war.
"It's an attempt to disinform the worldwide community", said Al-Iryani.More news: China ramps up crude oil imports despite Washington’s clampdown on Iran
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But leading Yemeni negotiator Ahmed al-Kawkabani told The Associated Press late Saturday that his team "won't recognize any redeployment outside what the United Nations proposed", which includes the removal of land mines, inspections and the end of all military presence at the port.
"Yes, it has begun", said United Nations spokesman Farhan Haq, when AFP asked whether redeployment of Houthi troops was underway.
Security concerns prevented the United Nations for months from accessing 51,000 tonnes of wheat in silos near Hodeidah that could feed millions in the impoverished country. The delay was blamed on administrative problems and bureaucracy.
The Iran-aligned Houthis say the government would try to choke them off if it gained control.
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.
"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.
"We will not accept this theatrical act and we will remain the main party in any agreement", al-Taher said.
Yahya Abu Hatim, strategic military expert, told Xinhua that Houthis usually precede any UNSC session on Yemen by declaring their acceptance to withdraw from Hodeidah and its key ports in an attempt to avoid any firm stance or decision against their behavior.
Members of the Houthi movement ride in the back of a vehicle during withdrawal from Saleef port in Hudaida province, Yemen May 11, 2019.