The main port used to feed Yemen's 30 million people is held by the Iran-aligned Houthi movement that also controls the capital Sanaa and has been battling against a Saudi-led Arab coalition seeking to restore a government ousted in 2014.
Hodeida has been the focus of fighting this year, raising global fears that a battle could cut off supply lines and lead to mass starvation. Yemeni forces backed by the Saudi-led coalition have massed on the city's outskirts.
Despite the ceasefire, one resident told Reuters he could hear the sound of missiles and automatic gunfire in the direction of the eastern 7th July suburb.
Houthi-run Al Masirah TV said coalition warplanes had launched two strikes on Ras Isa city north of Hodeida. The coalition did not immediately confirm the report.
The warring sides agreed after a week of consultations in Sweden to cease fighting in Hodeidah and withdraw their troops as part of confidence-building measures to pave the way for a wider truce and political negotiations.
It was the first significant breakthrough for UN-led peace efforts to end the nearly four-year-old war that has killed tens of thousands of people and pushed Yemen to the brink of famine.