Griffiths said, "It is time long past for us, together, to call for an early resumption of the political process, two years since the last round in Kuwait".
Al-Thawra Hospital, Yemen's biggest, was caught in the attack.
Kuwait's permanent representative to the U.N., Mansour Al-Otaibi, said that despite the announcement of the Arab coalition of a halt to its military operations to restore the port of Hodeidah, the Houthi militias continued targeting civilian and populated sites in Saudi Arabia by ballistic missiles.
Rebel-run media outlets have accused the coalition of carrying out Thursday s attacks in Hodeida.
Since Saudi-led bombing which began in 2015 more than 10,000 people have been killed and at least 40,000 wounded, mostly from Saudi-led air raids.
The campaign to take the city threatens to worsen Yemen's humanitarian situation as it is the main entry point for food, humanitarian aid and fuel supplies to the country.
"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".
"There is a war on children in Yemen - very few places are safe for a Yemeni child", she added.
But the coalition's spokesman, Turki al-Maliki, on Friday denied the charges, accusing the Huthis of having bombed the hospital and the fish market.
For the last few weeks, the United Nations had been trying to broker a deal in a bid to avert the attack and stop Saudi human rights violations, which it fears would further hinder Yemenis' access to food, fuel and medicine - worsening the world's most urgent humanitarian crisis.
"Every day this week we have seen new cholera cases in Hodeidah, and now this".
"The impact of the strikes is appalling".
On Friday, the UN's World Health Organisation said Yemen may be on the brink of a new cholera epidemic, with greater chance of a high death rate due to widespread malnutrition.
The video was shot amid stalling peace talks to slow the siege of the vital port city of Hodeidah. Yemen's government maintains that the rebels' "unconditional withdrawal" from Hodeida is key to restarting the talks.