"There has been complete calm since 03:00 a.m. Yemen time (1200 GMT) in the city of Hudaydah," a militant loyal to Yemen's fugitive former president Abd Rabbuh Mansur Hadi told AFP Tuesday.
The ceasefire agreement struck at the UN-sponsored peace talks in Sweden came into effect at midnight Monday but Saudi air raids continued after the deadline, residents in the city said.
The residents confirmed by phone that there has been no fighting between the pro-Hadi forces and Houthi fighters since 03:00 a.m.
But it was not possible to determine if the halt in fighting was in response to the ceasefire or just a temporary stoppage.
Residents said that daily fighting would usually be fierce in the evening and at night, before coming to a standstill at dawn.
The two warring sides have however welcomed the truce in the strategic Red Sea province.
The United Nations said Monday that the deal was to be implemented at midnight, even though the agreement reached in Sweden last week included an "immediate ceasefire" in Hudaydah and its surroundings.
A UN official, who requested anonymity, said the delay to the halt in hostilities was necessary for "operational reasons."