CAIRO — An internationally backed cease-fire in the key Yemen port of Hudaydah got off to a shaky start on Tuesday when fighting erupted moments after it took effect at midnight.

The clashes died down hours later, and by late Tuesday residents of the war-torn port were enjoying their first respite from a fight that has raged since June, displacing at least 550,000 people and leading to thousands of civilian deaths.

The truce, agreed to in Sweden last week by Yemen’s Saudi-backed government and its Houthi foes, is intended to ensure humanitarian access to Hudaydah, which is the conduit for 70 percent of aid to Yemen. The deal has stoked hopes the belligerents could start full-blown talks to end a war that has driven the Arab world’s poorest country to the brink of a humanitarian catastrophe.

But the cessation of hostilities, which followed a weekend of heavy combat in the city, is fragile. And the sporadic bursts of gunfire that rang out even late on Tuesday were a reminder that without concerted international support, heavy fighting could resume there.