Residents and government military sources have reported rebel snipers stationed on rooftops in civilian streets in eastern Hodeida, a few kilometres from the port on the western edge of the city. Amnesty's Lynn Maalouf said Monday that "as the battle for control of Hodeida intensifies, both sides seem intent on eviscerating the laws of war and disregarding the protected status of even the most vulnerable civilians".
Lowcock said the United Nations was ready to play a role in "ensuring the appropriate use of key facilities, especially around Hodeida" - a key entry point for humanitarian aid and vital supplies to Yemen.
The Sunni Muslim coalition led by Saudi Arabia and the United Arab Emirates has renewed its offensive on Hodeidah, a lifeline for millions of Yemenis, as Washington and London called for a ceasefire amid renewed U.N. -led peace efforts.
The port s deputy director, Yahya Sharafeddine, said the main entrance to the docks had been "the target of air raids" but was fully functioning.
Analysts however say a coalition attack on the docks remains a possibility, which would put at risk 14 million aid-dependant Yemenis already on the verge of mass starvation.
Four other port employees told AFP that one strike had killed a rebel commander and three of his guards, while a second strike had wounded another commander and his guards.More news: North Korea Plays Hardball to Get Sanctions Lifted
Almost 600 people have been killed since clashes erupted in Hodeida on November 1, ending a temporary suspension in a government offensive to take the city that began in June.
Western governments that support the coalition with arms and intelligence have toughened their stance on Yemen after the murder of journalist Jamal Kashoggi at the Saudi consulate in Istanbul on October 2 sparked a global outcry and opened Riyadh to possible sanctions.
Saudi Arabia and its allies intervened in the Yemeni government's fight against the Iran-backed Houthis in 2015, triggering what the United Nations now calls the world's worst humanitarian crisis.
There have been global outrage over the murder of US-based Saudi journalist Jamal Khashoggi, and after Democratic and Republican politicians had threatened to take action in Congress next week over the refuelling operations.
The World Health Organisation estimates almost 10,000 people have been killed in the Yemen war since 2015.
Hodeida port is under a near-total blockade by the coalition, who accuses Iran of smuggling arms to the Houthis.