He said many weapons have been smuggled to the Houthis through Hodeida and the small ports they control.
The blockade "is complicating what is already a catastrophic situation", McGoldrick said.
Saudi Arabia announced Monday that the Saudi-led coalition fighting Shiite rebels in Yemen will begin reopening airports and seaports in the Arab world's poorest country, days after closing them over a rebel ballistic missile attack on Riyadh.
The top United Nations aid official in Yemen called on the Saudi-led coalition on Tuesday to open all Yemen's sea ports urgently, saying it risked damaging the fight against cholera and hunger, with 7 million already in "famine-like conditions".
The coalition said Monday that it would reopen ports in areas held by allied forces and loosen restrictions it had tightened after the firing of the missile, which was intercepted near Riyadh's global airport.
McGoldrick says access to such ports is "helpful" but that the key need is access to the rebel-held Red Sea ports of Salif and Hodeida, closer to large population centers.
"Without Sanaa airport and Hodeidah and Salif seaports fully functioning and able to receive cargo, the dire humanitarian situation in Yemen will continue", Dujarric told reporters in NY.
Al-Mouallimi also accused the Houthis of diverting humanitarian aid "to fulfill their own requirements" and "to trade in the black market and achieve exorbitant profits at the expense of the Yemeni people". The Saudi closure had drawn worldwide condemnation and fears of a worsening humanitarian disaster in Yemen.
Flights between Egyptian capital Cairo and Yemen's port city of Aden resumed after an 8-day hiatus, according to an official of Yemen's national flag carrier on Tuesday.
The IS-claimed attack took place at a building in the Sheikh Othman district in the central part of the city.
Medical officials said six soldiers were killed, with the death toll expected to rise.
After two years of a devastating war, the Houthis still control much of Yemen's north while the south falls under the embattled President of Abed Rabbo Mansour Hadi, whose government is recognized by the global community and who is supported by the Saudi-led coalition.