The vehicles are currently parked near the Tienditas bridge, which remains blocked by Venezuelan troops.
President Nicolás Maduro, who has the support of the army, has rejected letting it into the country.
Opposition leader Juan Guaidó, who has declared himself interim president, has warned many Venezuelans are in danger of dying without international aid.
Mr Guaidó is head of Venezuela’s National Assembly and says the constitution allows him to assume power temporarily when the president is deemed illegitimate.
He has secured the backing of over 40 countries, including the US and most Latin American and European nations. Mr Maduro still has the support of China and Russia.
In other developments:
What’s the latest on the US humanitarian aid?
On Thursday, several lorries with food and medicine arrived at a collection centre in Cúcuta.
The vehicles were escorted by Colombian police motorcycles.
It was not immediately clear how the…