"The Secretary-General calls for prompt, effective and transparent investigations into these incidents to ensure accountability," Antonio Guterres' spokesman, Stephane Dujarric, said.
A detention centre holding migrants in Saada city was bombed on Friday. Basheer Omar, a Red Cross spokesperson in Yemen, said rescuers continued to search for survivors. He said more than 100 people had been killed and wounded, according to the Red Cross count.
Yemen's Houthi rebels and an aid group on Saturday claimed that the death toll had climbed to at least 82.
Doctors Without Borders (Medecins Sans Frontieres, or MSF) put the number of wounded alone at "about 200". Ahmed Mahat, MSF's head of mission in Yemen, said they had reports of "many bodies still at the scene of the air strike, many missing people".
Another Saudi air raid on Friday in the port city of Hodeidah - later confirmed by satellite photos analysed by the AP news agency - hit a telecommunication centre that is key to Yemen's connection to the internet. Early on Saturday, the internet remained down.
Yemen's Houthi Health Minister Taha al-Motawakel has appealed to the international community for medical aid. He accused the Saudi coalition of deliberately targeting civilians.
The Houthi Al Masirah TV satellite news channel said the strike on the telecommunications building killed and wounded an unspecified number of people. It released chaotic footage of people digging through rubble for a body as aid workers assisted bloodied survivors.
Save the Children said at least three children were killed in the Hodeidah attack.
Air raids also hit near the capital, Sanaa, held by the Houthis since late 2014. On Tuesday, at least 14 people were killed in Saudi air raids in Sanaa.
The intense campaign comes after the Iran-backed Houthis claimed a drone and missile attack that struck inside the United Arab Emirates capital earlier this week - a major escalation in the conflict in Yemen where the Saudi-led coalition, with the UAE as a member, has been carrying out air raids since 2015.