Britain, Germany, France and Spain and more than a dozen other European Union member states recognised Mr Guaido in a coordinated action on Monday, following the expiration of an ultimatum they gave for Mr Maduro to hold a new presidential election.
The bridge, which connects Cucuta and the city of Urena in Venezuela, remains blocked after the Venezuelan military, earlier this week, placed cargo containers and a tanker lorry across the road surface.
Maduro has refused the aid, disavowing any humanitarian crisis and saying Venezuela is not a country of beggars.
On Wednesday the Venezuelan military, which backs Maduro, barricaded its own side of the border, vowing not to allow the aid to enter.
Venezuela is in the midst of a power struggle following the National Assembly's declaration that Maduro is an usurper, and several countries - including the US - now recognize opposition leader Juan Guaido as the nation's legitimate president.
This is the first aid to arrive and would only last for a short time, but officials said it would benefit thousands of people unable to get hold of basic medicine and food inside Venezuela.
Toledo on Friday appealed to the armed forces.
"We may have different points of view and understandings of the causes of this crisis, but we share a similar objective: to contribute to a political, peaceful and democratic solution", said Mogherini.
Guaido, a previously largely unknown opposition leader, has been recognized by Australia, Canada, a group of major European nations, a number of Latin American countries and the United States, which have upped sanctions on the country.
Venezuela has been rocked by protests since January 10 when Maduro was sworn in for a second term following a vote boycotted by the opposition.
'They offer us toilet paper, like Donald Trump threw at the people of Puerto Rico, ' he said at the conference, which experienced technical difficulties including a blackout and a microphone failure.
"If they dare to keep blocking the routes, and creating obstacles to the lives of Venezuelans, we'll go to open them, with the people, the security forces", Guaido said. "We have recently revealed a conspiracy to stage a coup, funded and supported from Colombia", he noted. Unlike many other news organizations, we have not put up a paywall.
Consultants Eurasia Group said on Thursday that Maduro's traditonal allies Russian Federation and China are "unlikely to lend (him) meaningful support", reinforcing its view that the socialist leader "will be unable to sustain his regime".
Foreign Ministry spokeswoman Hua Chunying's statement comes in response to a question about a meeting Thursday of an "International Contact Group" led by Uruguayan President Tabare Vazquez and attended by leaders of 14 countries, including Spain, Italy, Portugal and Sweden.
German Foreign Minister Heiko Maas also said Germany had earmarked €5 million ($5.72 million) worth of assistance for Venezuela.