According to the UN's office for the Coordination of Humanitarian Affairs (OCHA) on Tuesday, 34 people were killed among 92 civilian casualties in the first week of November in Hodeida province.
Mariam Aldogani, Save the Children's field coordinator in Yemen, said that the people in Hodeida are living in a "state of fear".
He urged all parties to relaunch peace talks, which were abandoned in September.
Tuesday's announcement follows Foreign Secretary Jeremy Hunt's visit to Saudi Arabia and the United Arab Emirates.
After almost four years of conflict in Yemen, home to what the UN calls the world's worst humanitarian catastrophe, the United States and Britain are now pressing Saudi Arabia and its allies to end the war against the Iran-backed Huthi rebels.
In France, Foreign Minister Jean-Yves Le Drian said it was time "the global community said enough is enough".
Aid groups fear for the safety of almost 6,00,000 people living in Hodeida - and for millions of others dependent on its port for what little food and humanitarian aid trickle into impoverished, blockaded Yemen.
Speaking to AFP earlier, a military official said pro-government forces had temporarily stopped their advance into the port to allow safe passage for civilians, humanitarian staff and wounded.
"Most of the momentum we have seen on the frontlines in the previous year has been along the Red Sea coast, leading northward to Hodeida - the biggest strategic prize", said Elizabeth Dickinson, senior analyst with the International Crisis Group.
Medics in hospitals across the city reported 110 rebels and 32 loyalist fighters killed overnight.
The Huthi rebels and Saudi-led coalition bring very different strengths to a complex conflict.
"They have repeatedly argued that taking Hodeida out of Huthi control would reduce the rebels' income and encourage them to negotiate in good faith".
Clashes between Saudi-backed troops and rebels in Hodeida have raged for almost two weeks, leaving almost 600 people dead and prompting warnings from the United Nations of catastrophic devastation if fighting escalates.
The Saudi-led coalition has also come worldwide pressure to end the conflict following the killing of Saudi dissident journalist Jamal Khashoggi in his country s consulate in Istanbul on October 2.
Multiple countries, including Germany and Norway, have announced the suspension of arms sales to Saudi Arabia after Khashoggi's killing.
United Nations mediator Martin Griffiths - whose efforts to host negotiations in Geneva in September failed - met with Yemeni Foreign Minister Khaled al-Yamani in Riyadh for talks on reviving the peace process, Saudi Arabia's state news agency reported.
The port has been under blockade by the Saudi-led coalition for a year.
The Saudi-led coalition has been waging a war in Yemen since March 2015 to push back the Iran-backed Huthis, but the rebels still hold Hodeida and the capital Sanaa.