The Houthi rebel pullout from the ports of Hodeidah, Saleef and Ras Isa on Saturday was "in accordance with established plans" and would be verified on Tuesday, the UN said.
"All three ports were monitored simultaneously by UN teams as the military forces left the ports and the coastguard took over responsibility for security," the UN said on Sunday.
Military equipment is expected to be removed in coming days and de-mining is also planned.
Formal verification of the first withdrawal will take place at the three ports on Tuesday, the UN said.
The head of the UN monitoring team in Hodeidah had assured the government on Saturday that the rebel withdrawal would be carried out according to agreements.
Danish Lt Gen Michael Lollesgaard briefed government representatives in Aden after the Houthi rebels announced a unilateral withdrawal from the Red Sea ports earlier in the day.
"The meeting was positive," Col Wathah Al Dubaish, spokesman of the joint government forces in Hodeidah, told The National.
"Gen Lollesgaard provided essential clarifications regarding the unilateral pullout by the Houthis.
"He assured the head of the government team that the withdrawal process would be according to the latest version of the agreement signed by all of the parties."
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 UN supervision.
Gen Lollesgaard chairs the committee of government and rebel representatives that is meant to oversee its implementation.
The general and Maj Gen Sagheer Aziz, head of the government delegation on the Redeployment Co-ordination Committee, agreed on a "clear mechanism and clear schedule for the withdrawal process and the start of clearing mines from the ports", Col Al Dubaish said.
The ceasefire was agreed at UN-brokered talks in Sweden in December but its implementation has been delayed by mistrust between the warring parties.
It will allow the flow of food and humanitarian aid into Yemen, where millions of people are on the verge of famine after four years of war.
Col Al Dubaish said Gen Aziz told Gen Lollesgaard that the rebel withdrawal must be monitored by the UN and that a government team that would visit the ports to verify that it was being done according to the Stockholm agreement.
“The Houthi militia must withdraw from the wharves and from around the ports completely," Col Al Dubaish said.
"They have to be redeployed to Al Gabbana, an area five kilometres north of Hodeidah city, according to the withdrawal agreement."
He said 25 more UN ceasefire monitors arrived in Hodeidah on Saturday as rebels began their withdrawal.
The Security Council approved sending 75 observers to Hodeidah four months ago but only 15 had arrived before Saturday. The delay was blamed on administrative problems and bureaucracy.
"Most of the UN monitors who have arrived are German, Dutch and Danish observers," Col Al Dubaish said.
Government officials have questioned whether the Houthis are actually withdrawing from the ports or simply handing over to control rebel fighters in disguise.
Yemeni Information Moammar Al Eryani on Saturday described the operation as an attempt to mislead the international community, which has been increasing pressure for an end to the war.
"What happened today is a flagrant show, a group of militiamen left and they were replaced by others wearing coastguard police uniforms," Mr Al Eryani said.
Waleed Al Qudaimi, deputy governor of Hodeidah province, told The National that the Houthis were trying to avoid criticism at a Security Council session on May 15 by repeating the ruse they had tried in late December.
“They took this fake step to avoid being identified as the party responsible for hindering the peace process in Yemen,” Mr Al Qudaimi said.
Despite the attempts at a ceasefire in Hodeidah, which the UN hopes will lead to another round of peace negotiations, fighting continues elsewhere in Yemen.
In Dhalea on Saturday, the joint Southern Forces stormed Houthi posts in Qatabah city as they continue to push back a rebel incursion into the government-controlled province.
"Our forces, along with divisions from the First Brigade and the special forces, cleared the Houthi snipers who stormed the headquarters of the economic corporation and the base of the central security forces in northern Qatabah," an officer in the Security Belt forces told The National.
Dozens of Houthi fighters were killed, including two high-ranking officers, he said.
Col Ahmed Qaid, commander of the Security Belt forces in Dhalea, said the operation was launched after Houthi attempts to advance, all of which failed and resulted in the deaths of hundreds of rebel fighters.
About 600 rebels have been captured, including four commanders, Col Qaid said.
