The appeal came as fighting intensified in the key rebel-held Red Sea port city of Hodeida, despite growing worldwide pressure to end a conflict that has left the country on the brink of starvation.
The military operation achieved significant progress on the ground and drove the Houthi rebels out of key areas in Hodeidah, Saba said.
The bloodshed comes despite growing global pressure to end a years-long conflict that has left thousands dead.
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.
A pro-government medical source said that mortar shells landed on residential areas and caused casualties among citizens.
'Yemen is today a living hell - not for 50 to 60 per cent of the children - it is a living hell for every boy and girl in Yemen, ' he told a news conference in the Jordanian capital.
Yemen's internationally recognised government On Thursday welcomed a call from the U.S. for peace in the conflict-torn country, state-run news agency Saba said.
U.S. criticizes Turkey strikes on Kurd militia in Syria
Ankara considers the militia a terror threat and an extension of Kurdish rebels waging an insurgency within Turkey. Conducting joint patrols is seen as a way to tamp down potential violence between the various groups in the area.
The United States and Britain have called for an end to the conflict, raising pressure on Saudi Arabia as it faces a global outcry over the murder of prominent Saudi journalist Jamal Khashoggi in the Saudi consulate in Istanbul on October 2.
Hodeida port is the entry point for more than 70 percent of imports into the impoverished country, which is teetering on the edge of starvation.
Mr Hunt echoed UN Secretary-General Antonio Guterres, who on Friday appealed for an end to the war and said recent political developments had created signs of hope for a settlement.
The United Nations has listed Yemen as the country with the world's biggest humanitarian crisis, with 7 million Yemenis on the brink of starvation and cholera causing more than 2,000 deaths.
"The only way to enable refugees to return home, and to bring down the overall numbers worldwide, is to end conflicts themselves".
The interview was broadcast four days after the Trump administration demanded a cease-fire and the launch of United Nations -led political talks to end the Yemen conflict, which has devolved into a proxy war between the Saudis and Iran.
A previous attempt to take the city in June ran into difficulties and was halted ahead of UN-led peace consultations in Geneva which collapsed in September after the Houthis failed to show up.
The Yemeni government is seeking to expel Houthi rebels out of the strategic city of Hodeidah in recent days despite warnings by worldwide humanitarian agencies.