The coalition has deployed thousands more troops since last Thursday to retake the port, a key entry point for Iranian-supplied arms and ammunition, including parts for missiles used to attack Saudi Arabia.
The Houthi official responsible for foreign affairs, Hisham Sharaf, praised Griffiths' continued efforts, but urged Western governments to take concrete steps to enforce a ceasefire to create "conditions conducive to peace far away from any pressure or dictates", the Houthi-run Saba news agency said.
The regional director of the United Nations children's agency, Geert Cappelaere, said the warring sides in Yemen make it hard to deliver and distribute humanitarian aid to the country.
Saudi Arabia, an ally of the U.S. - which sells weapons worth billions of dollars and provides logistical support to the coalition - has come under heavy criticism for its conduct of the war that has left thousands dead and injured. "Yemen is today a living hell - not for 50% to 60% of the children - it is a living hell for every boy and girl in Yemen", he said.
On Wednesday, the UN Special Envoy for Yemen Martin Griffiths announced his commitment to bringing the warring Yemeni parties to the negotiation table within a month, stressing that dialogue remains the only path to reach an inclusive agreement in the country.
Three-quarters of Yemen's 29 million people are food insecure, 1.8 children suffer from malnutrition and 400,000 children under age 5 are in the worst stage of malnutrition - without intervention they might die.
Thirteen pro-government troops were killed, medical sources in Aden and Mokha - where the fighters were transported.
According to the World Health Organization, almost 10,000 people have been killed in the conflict, though some rights groups estimate the toll could be five times higher.
Almost three quarters of the country's imports flow through Hodeida, from where they are transported by land to areas further north.
The clashes erupted just hours after the government said Thursday it was ready to restart peace talks with the Iran-backed Huthis.
The Yemeni government is seeking to expel Houthi rebels out of the strategic city of Hodeidah in recent days despite warnings by global humanitarian agencies.
According to the World Health Organisation, almost 10,000 people have been killed in the conflict since 2015.
UN Secretary-General Antonio Guterres on Friday called for a halt to violence in Yemen to pull the country back from a "precipice" and build momentum toward talks on ending the war.