The European Union condemned Venezuela's use of violence and armed civilians to block the aid entry, while United Nations Secretary-General Antonio Guterres said he was "shocked and saddened" by the civilian deaths.
Guaido, the 35-year-old leader of Venezuela's National Assembly, declared himself acting president in January after the opposition controlled legislature concluded that Maduro was fraudulently re-elected.
Some 50 countries recognize him as Venezuela's legitimate president.
Guaido flew to the Colombian capital Sunday for the meeting with members of the Lima Group - 13 Latin American countries plus Canada that are seeking to resolve Venezuela's political impasse.
Vice President Mike Pence will represent Washington at the event.
US Secretary of State Mike Pompeo said he was confident that "Maduro's days are numbered," blaming the border violence on armed civilian loyalists known as "colectivos."
"We're aimed at a singular mission -- ensuring the Venezuelan people get the democracy they so richly deserve," Pompeo said on CNN's "State of the Union."
President Donald Trump has said the United States is not ruling out armed action.
Upon landing in Bogota Guaido called on the international community to consider "all measures to free" Venezuela.
This is the first time that the Lima Group, which first met in the Peruvian capital in 2017, will speak directly to Guaido.
Venezuela is in the midst of a humanitarian crisis that has seen poverty soar during a prolonged recession and hyperinflation.
Humanitarian aid, much of it from the United States, has been at the center of the standoff between Maduro and Guaido.
Maduro claims the aid is a smokescreen for a US invasion, and has ordered several crossings on Venezuela's borders with Colombia and Brazil closed.
"Today we consolidated yesterday's victory, tomorrow we'll consolidate it even more," Maduro's right-hand man Diosdado Cabello said Sunday at a pro-government rally in the border town of Tachira.
"Not a single one of those trucks with aid got through," Cabello said.
Maduro seems to have won this round in the power struggle, even though 156 members of Venezuela's security forces deserted to Colombia or Brazil.
After Saturday's events it is "not very clear" that Guaido has "massive" support in Venezuela, analyst Rafael Pineros told AFP.
However the events, which also led to increased repression by the Maduro regime, may instead result in a forceful foreign intervention in Venezuela, according to political scientist Laura Gil.
"In the Lima Group the consensus is that Maduro must be removed, but there is no consensus on how to do that," Gil told AFP.
Another winner is Washington, because the only way to justify a use of force, if they are willing to actually do that, "is by invitation," she said.
Colombian President Ivan Duque visited the two border crossing points where most of the violence took place on Saturday.
A 14-year-old boy was among those killed Saturday near the Brazilian border in clashes with Venezuelan security forces. More than 300 people were injured in a day of disturbances at crossings on the Colombian and Brazilian borders.
Sporadic clashes between hooded protesters and police, supported by terror-spreading armed civilian "colectivos," continued Sunday on the Venezuelan side of the border, but were not as intense as the day before.
Scores of Venezuelans who managed to slip across the border to get aid were trapped there as Venezuelan authorities had closed the border.
Nicolasa Gil, a frail 71 year-old who spent the night in Cucuta near one of the crossing points, said she was "scared to cross into my country.
"Here we're safer than over there," she told AFP.
The attempt to cross aid stockpiled in Colombia led Maduro to sever ties with Bogota - and on Sunday, a group of Colombian diplomats trickled across one of the border bridges on foot, luggage in tow.
Also Sunday three Bolivarian National Guard sergeants fled Venezuela and sought refuge in Brazil.
In the barracks "there is no food," said one of the defectors, identified as Carlos Eduardo Zapata.
"They don't even have mattresses. Us National Guard sergeants are sleeping on the ground."
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