Since 2015, Saudi Arabia has been leading a military campaign to restore the internationally recognised government to power and push back the Huthi rebels, who still hold the capital Sanaa.
On June 13, the Yemeni government forces, backed by the Saudi-led coalition, launched an offensive to seize the port of Hodeidah from the Shia Houthi rebels.
"This is a tragic reminder that in Yemen the global humanitarian law - in place to protect civilians and civilian infrastructure in times of war - continues to be broken on a daily basis".
Missiles hit the crowded fish market, which is a few hundred meters from the city's main hospital.More news: Donald Trump taunts basketballer LeBron James in late night Twitter rant
The Yemeni government and rebel opposition Houthis have both declared their willingness to attend UN-organised peace talks in Geneva next month.
"This crime is not the first one committed by the Houthi militias against civilians in Hodeidah or elsewhere by indiscriminate bombing of residential neighbourhoods", he said.
Last month they said they were pausing the assault to give United Nations mediation efforts a chance.
"These airstrikes are putting innocent civilians at extreme risk", Lise Grande, the United Nations humanitarian coordinator for Yemen, said in a statement.
"Hospitals are protected under global humanitarian law".
Saudi Arabia suspended oil exports through the channel following last week's Houthi attacks on crude tankers.More news: Turkish lira skids past 5 to dollar on USA sanctions move
The statement also emphasized that the "barbaric crimes" against Yemeni women in Hudaydah were not possible without the United States government's approval.
Yemen's civil war began in 2014.
World Health Organization officials on Friday called on the sides to halt fighting for at least three days for a vaccination effort that aims to prevent another deadly wave of cholera.
"The impact of the strikes is appalling".
Other Hodeidah residents, who asked to not to be named, said they heard mortars being fired from a rebel base near the hospital just before the news broke of the attack.
Appointed past year to lead UN peace efforts in Yemen, Griffiths said there had been progress in talks on a possible deal with the Huthis to turn over control of the port to the United Nations "but the gap is not closed".More news: No, Google is not returning to China, censored or otherwise