During the two-month truce, the Saudi-led coalition will allow 18 vessels carrying fuel into the port of Hodeida, and two commercial flights a week from the Yemeni capital to Jordan.
Fighting also raged between Yemen's government forces and the Houthis elsewhere including in the provinces of Jawf and Taiz, military officials say.
UN special envoy Martin Griffiths told the Security Council that there had been a dramatic deterioration in the more than six-year-long war with a Houthi offensive on Marib, putting millions of civilians at risk.
The raids in Yemen's rebel-held capital come after the coalition said it intercepted 10 drones launched by the rebels on Sunday, in a sharp escalation in cross-border attacks on the kingdom.
More than 20 Yemeni farmers are reported to have been killed in what locals are calling a process of 'colonisation' by the Houthis.
The sudden spike in violence across long-stalemated front lines threatened to exacerbate the five-year conflict and complicate indirect peace talks between Saudi Arabia and the Iran-backed rebels.
UNICEF said that militias allied with the Saudi-led coalition fired at Houthi-held positions in the hills surrounding the Yemeni city of Taiz, killing at least seven children.
At least 190 people have died of the disease so far this year and 100,000 more cases of suspected cholera have been reported in Taiz and adjacent cities.
Houthi rebels have blocked roads linking the cities of Taiz and Hudaida, denting efforts to provide aid in a war-torn country where almost 14 million Yemenis are on the brink of famine.
Though the warring factions agreed on several issues in Sweden, Yemenis are still waiting to see if the agreement comes into effect.
Firearm sales are brisk across the country as weapons dealers lure poverty stricken Yemenis to sell off their personal guns.
Safa Sadeq, a 10-year-old Yemeni girl, has been confined to her bed after she was targeted by a Houthi sniper while looking after sheep at her family's farm in Taiz.
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