But the Venezuelan military has blocked the Tienditas International Bridge linking the two countries with two shipping containers and a tanker, which has become a symbol of Maduro's standoff with the United States and its European and South American allies.
He said three more warehouses would be opening up in the region shortly and that his countrymen could count on aid arriving "as soon as they open the border gates in the next few days".
The items were being packed by volunteers into individual bags for Venezuelan families. The first shipment includes food kits for 5,000 Venezuelans and high-protein nutritional supplements that can treat an estimated 6,700 young children with moderate malnutrition.
China says peaceful dialogue and political means are the "only way" toward enduring peace in Venezuela and says it backs multinational efforts toward that end.
Opposition leader Juan Guaido has declared himself interim president in Venezuela, a move recognized by several dozen countries, but Preside11:15 nt Nicolas Maduro is refusing to relinquish power.
"We will succeed in letting the humanitarian aid in, because it's about saving lives", Guaido posted on his official Twitter feed.
"We do not agree with the content of the document", Maduro said. But the aid blockade could lead to troops disobeying Maduro's orders and allowing the much-needed aid to pass.
"Any potential political use of humanitarian aid can generate risks, in particular for those the aid is meant to support", said the letter, signed by 15 non-governmental organizations, including Oxfam, Mercy Corps and Save the Children.
Abrams, a long time Republican foreign policy player who helped steer Ronald Reagan's controversial backing of anti-communist forces in Central America - said that countries should only deal with Guaido.
Under Maduro's rule, Venezuela has endured one of the deepest economic collapses in recent history, with hyperinflation and ever-worsening shortages.
Guaido's representative in Cucuta, Lester Toledo, said the provisions already delivered were the "first drops" and promised "a tsunami of humanitarian aid" would follow.
The nation is "not suffering the humanitarian crisis fabricated by Washington over the last four years to justify intervening in our country", Maduro added. But Maduro has refused calls for him to step down, insisting Washington is orchestrating a coup against his government.
"There's an attempt to violate our national sovereignty with this "show" of a humanitarian operation by the government of Donald Trump", he said.
Guaido has said the time for dialogue has passed. Her sign reads, "In the name of God, we declare peace and freedom for our attractive Venezuela. The other practical problem we face is that, given the sanctions, we should no longer manage Venezuela from the United States ... but from Europe".
Jose Mendoza, 22, held up the poster that Perez had made earlier, which stated, "in the name of God, we declare peace and freedom for our lovely Venezuela".
USAID has begun packaging pallets of foodstuffs after Bolton's announcement last week that it would send humanitarian aid.