Opposition leader Juan Guaido called the Youth Day demonstrations to honor 40 people killed in anti-government rallies and press for the food and medicine to be brought into the economically-ravaged South American country.
While waiting for the National Assembly leader to speak in east Caracas, his supporters chanted: "Freedom!"
"We're asking the military authorities to let in the aid and to protect it so that it reaches those most in need," Juan Perez, 68, told AFP.
Guaido, who stunned the world on January 23 when he declared himself acting president, said the protest would "demand the entry of humanitarian aid that will save the lives of more than 300,000 Venezuelans." Taking his authority from the constitution, Guaido says Maduro's presidency is "illegitimate" as it was founded on flawed elections.
He is trying to force the socialist leader from power so he can set up a transitional government and hold new presidential elections.
Maduro meanwhile called a march of young leftists in the center of Caracas denouncing foreign intervention in Venezuela's affairs and collecting signatures of people who reject US President Donald Trump.
The fate of tons of aid piling up in Colombian collection centers at the border with Venezuela has become central to the power struggle between Guaido and Maduro, who is backed by the powerful armed forces.
Venezuela is in the grip of recession and hyperinflation while millions of people are suffering from a shortage of basic necessities. The UN says some 2.3 million people have fled since 2015.
But the military has barricaded a border bridge linking the countries, with Maduro describing the aid as a "political show" and a pretext to a US intervention.
Guaido, recognized by some 50 countries as interim president, has offered amnesty to military personnel who dump Maduro and told them that refusing to allow in aid was a "crime against humanity."
He says almost 100,000 Venezuelans have signed up as volunteers to help bring in aid and distribute it to those most in need.
"The military are the ones keeping Maduro in power. I call on them to reflect and take the side of the people suffering from hunger," said protester Maria Ballera, 75.
The Venezuelan government distributed food and medicine on Monday.
Guaido's envoys met Brazilian officials in Brasilia on Monday and announced plans to establish a second aid storage center in the state of Roraima, on Venezuela's southeastern border, from next week.
But Defense Minister Vladimir Padrino said the armed forces were deploying a "reinforced presence all along the border."
Although he has wide international support in his bid to oust Maduro, Guaido needs the backing of the armed forces.
He has warned the military that it will be held responsible for any deaths among the protesters on Tuesday.
The US has presented a draft resolution to the UN Security Council calling for international aid deliveries and new presidential elections.
Russian Foreign Minister Sergei Lavrov on Tuesday dismissed the move as an attempt to "cover up planned provocations... to destabilize the situation in Venezuela and even gain an excuse for direct military intervention."