The military coalition tightened its blockade in Yemen this week after a ballistic missile fired by Houthi rebels was intercepted near the Saudi capital, Riyadh.
"A number of measures have been introduced recently by the coalition effectively closing air, sea and land access to Yemen", Lowcock said.
"We ask the Saudi-led Coalition to facilitate unhindered access of aid workers to people in need, in compliance with global law, by ensuring the resumption of all humanitarian flights", the aid groups said.
Yemen is facing a mass starvation that will affect millions of lives unless the Saudi-led coalition ends its blockade and allows aid deliveries into the country, the United Nations aid chief has warned.
Since August 2014, Yemen has remained devastated in a conflict between the governmental forces and the Houthi insurgents.
The Saudi-led Arab military coalition intervened in Yemen in March 2015 to support President Abedrabbo Mansour Hadi after the Houthis forced him into exile.
The war has killed more than 10,000 Yemenis, mostly civilians, and displaced more than 3 million others, according to United Nations agencies.
The conflict has led to a humanitarian disaster in the country.
At least 50 people, including civilians, were killed and injured in fresh Saudi-led coalition airstrikes on a village in Yemen's northwest province of Hajjah on Tuesday, a provincial security official and medics said. Seven million are on the edge of hunger and two million children are short of food.
Noting that the current stock of vaccines in the country will only last one month, the organizations said: "If it is not replenished, outbreaks of communicable diseases such as polio and measles are to be expected with fatal consequences, particularly for children under five years of age and those already suffering from malnutrition".