"Humanitarian movements into Yemen remain blocked," said Russell Geekie, spokesman for the UN office for the coordination of humanitarian aid OCHA.
"The reopening of the port in Aden is not enough. We need to see the blockade of all the ports lifted, especially Hodeida, for both humanitarians and for commercial imports."
The coalition shut down Yemen's borders on Monday in response to a missile attack by Houthi rebels that was intercepted near Riyadh airport.
UN aid chief Mark Lowcock told the Security Council this week that unless the blockade is lifted, Yemen will face "the largest famine the world has seen for many decades, with millions of victims."
After an outcry from the United Nations, the coalition on Wednesday reopened Aden, which is controlled by pro-Saudi government forces, and on Thursday opened the land crossing at Wadea on the Saudi-Yemen border.
But Geekie said no aid had gone into Aden yet and the reopening of the Wadea crossing did not affect UN operations.The transport minister of Yemen's internationally recognised government, Murad al-Halimi, said that two airports in the loyalist-held southern cities of Aden and Seiyoun would also reopen from Sunday, Yemeni media reported.
He said national carrier Yemenia would resume its flights to and from the two airports, from where it flies to destinations including Amman and Cairo.
Meanwhile, the sea port at Hodeida, which is in rebel-held territory, is key to UN aid efforts as it is closest to the majority of people in need
The coalition accuses rebels, who are allied with the former President Ali Abdullah Saleh, of using aid shipments to smuggle in weapons.Before the blockade, UN aid agencies were delivering food and medicine through Hodeida, Saleef and Aden ports.
"There can be no alternative for all these ports being fully functional and receiving commercial and humanitarian cargo," said the spokesman.
The United Nations has listed Yemen as the world's number one humanitarian crisis
, with 17 million people in need of food, seven million of whom are at risk of famine.
More than 2,000 Yemenis have died in a cholera outbreak now affecting nearly one million people.
Saudi Arabia and its allies intervened in neighbouring Yemen in March 2015 to push back the rebels who control the capital Sanaa, in an attempt to restore the government of Abedrabbo Mansour Hadi to power.
But the military intervention, which has triggered widespread criticism from the international community, has left more than 10,000 people, most of which civilians, dead.