VIVOplay TV channel reported on Thursday that first containers with humanitarian aid have arrived to the Colombian city of Cucuta at the Venezuelan border.
The items were being packed by volunteers into individual bags for Venezuelan families.
Juan Caicedo, a spokesperson from Migration Colombia, Colombia's Ministry of Immigration and Immigration Control, said the Venezuelan military put the blockade into place Tuesday afternoon, adding that there are cameras monitoring activity on the bridge.
The report comes after the European Union and a group of Latin American governments which kept a moderate line following the political crisis which has engulfed Venezuela called for dialogue and fresh elections.
"I am convinced that the way we are going to pass this aid is with the Venezuelan people", Toledo said at a press event unveiling the aid.
The United States bends the definition of "humanitarian aid" to advance its political interests in Venezuela.
"Venezuela will not allow the show of. humanitarian aid because we do not beg from anyone", Maduro told reporters.
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"Dear military personnel, this aid is also for you. here comes food for your children, here comes medicine for the people who are suffering", he said.
"I think it is better for the transition to democracy in Venezuela that he'd be outside the country, and there are a number of countries that I think would be willing to accept him", he stated.
Venezuela's socialist economic system has been severely hit following the collapse of world oil prices in 2014.
Venezuela is already experiencing mass hunger, and is likely to experience even greater difficulty importing food thanks to stepped-up USA sanctions. Venezuela has gone from being one of the richest countries in the region, to the poorest.
When asked how US aid might make it into Venezuela, a spokesman for the US Agency for International Development said the United States was working with Guaido on a plan, but did not disclose any details.
However, he emphasised that there was no turning back from regime change in Venezuela.
Maduro accuses Trump of "disrupting noble dialogue initiatives", which were promoted by Uruguay and Mexico and backed by the Caribbean Community (CARICOM).
Omaria Perez, 44, was at the entrance of the Tienditas bridge early on Friday morning, writing messages on placards.
Medina told a news conference at United Nations headquarters in NY: "I think we need the strength of the U.S., Brazil, Colombia".