The UN special envoy for Yemen, Ismail Ould Cheikh Ahmed, had announced on Monday that the cessation of hostilities would take effect "at 23:59 (local time) on 19 October 2016, for an initial period of 72 hours, subject to renewal".
It is the sixth attempt to end the bloodshed since a Saudi-led Arab coalition intervened in March 2015 to support the government of President Abedrabbo Mansour Hadi after rebels overran much of Yemen.
Shortly after the truce began, the coalition issued a statement saying it "will abide by the ceasefire", which aims for "distribution of the greatest possible humanitarian and medical assistance" to Yemen's people, especially the besieged city of Taez.
The rebels' military spokesman, General Sharaf Lokman, said his forces will respect the ceasefire as long as "the enemy" also abides by it on land, sea and air.
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However, he urged his fighters to be ready to retaliate against "all aggression."
Less than an hour after the truce took effect fighting continued, notably around Yemen's third city, Taez. Rebel bombardments of some districts there led to clashes with loyalist forces, military sources and residents said.
Pro-Hadi positions also came under fire in Sarwah, east of Sanaa, loyalist military sources said.
Almost 6,900 people have been killed -- more than half of them civilians -- while another three million are displaced and millions more need food aid.
EU foreign policy chief Federica Mogherini late yesterday said the truce should be a first step towards resuming UN-led peace talks.
"The ceasefire must be respected by all sides and its duration extended so as to create the necessary conditions for such negotiations," she said.
Mogherini added the ceasefire will allow urgent humanitarian assistance to reach large parts of the population that have suffered drastic shortages.
The last ceasefire attempt, which began in April alongside UN-brokered peace talks in Kuwait, failed with both the rebels and the coalition accusing each other of breaches.
After peace talks collapsed in August, fighting escalated until an October 8 coalition air strike which the UN said killed more than 140 people and wounded at least 525 at a funeral in Sanaa.