"We Venezuelans shall return to the streets ... to demand the entry of humanitarian aid which will save the lives of more than 300,000 Venezuelans now at risk of dying", Guaido tweeted late Monday.
They urged President Maduro to allow humanitarian aid in - while government supporters also rallied in the capital, Caracas.
The struggle now centers on emergency food and medicine from the United States warehoused on the Colombian border town of Cucuta.
Draped in Venezuelan flags, his supporters carried signs saying "No more dictatorship", and "Leave the country, damned tyrant".
While resisting overwhelming Western pressure, Maduro has consistently said he believes in "dialogue and mutual understanding" between all Venezuelans.
And standing on the Venezuelan side of the Tienditas Bridge - with the aid stockpiled just 1km on the Colombian side - the MPs raised their fists in defiance of the global community and proclaimed; '!No Pasaran - It Will Not Get Through!'
"Nicolas Maduro should put his hand on his heart and accept that aid", said Mayerly Prada, among a small group of protesters on the Colombian side of the Tienditas International Bridge.More news: Morris sounds off after Celtics' collapse
The opposition will also hold an all-night vigil on Tuesday in a Caracas square to demand that Maduro let aid in. "It's our money. With that, we could solve all our country's problems".
Guaido is trying to oust Maduro from office so he can establish a transitional government and hold new presidential elections.
The administration of U.S. President Donald Trump has said all options are on the table for Venezuela and has not ruled out military intervention, although it says its aim is "a peaceful transfer of power".
"I'll be on the streets until this is over", said Cecilia Navarrete, 50, at his rally on Tuesday.
'The few supplies that they have stored in Colombia is nothing, ' Mr Parada, 32, who represents the town of Capacho Viejo, close to the Colombian border, told MailOnline.
FILE PHOTO: Venezuelan exiled veteran opposition figure and former mayor of Caracas Antonio Ledezma wears an Order Medal Of Cruzeiro Do Sul after receiving it form Brazil's Foreign Minister Aloysio Nunes Ferreira (not pictured), at the Itamaraty Palace in Brasilia, Brazil April 27, 2018. Her brother, sister and father are among the estimated several million who have emigrated in recent years, fleeing the crisis.
Washington has said it will turn over control of those resources to Guaido once Maduro has been removed from power.
"The economic war [from the U.S.] is asphyxiating the country, causing much suffering amongst the most vulnerable", de Zayas said in a recent interview with L'Anti Diplomatico.
While Venezuela once had one of the largest Jewish communities in the region, numbering some 25,000 in 1999, only about 6,000 Jews are believed to remain in the country, with numerous rest having fled to Israel, Canada, the United States and elsewhere.