Maduro has overseen an economic collapse in the oil-rich OPEC country that has left many Venezuelans malnourished and struggling to find medicine, sparking the exodus of an estimated 3 million Venezuelans.
A few trucks of food and medicines are now blocked on the Colombian border.
Guaido has accused Maduro's troops of being complicit in a crime against humanity by blocking food and medical care.
Luis Escobar, a Venezuelan who now lives in Colombia after fleeing his crisis-ridden nation, said his wife has advanced breast cancer and urged Maduro to accept the aid.
Guaido says the May 2018 vote in which Maduro won a second term as president was a sham and on January 23 invoked a constitutional provision to declare himself president, promising free and fair elections.
While the 35-year-old has the support of powerful western nations, other global powers such as Russia, China and Turkey continue to back the Maduro regime and have denounced what they call foreign meddling in Venezuela's internal affairs.
Earlier, Maduro vowed not to let in "fake humanitarian aid" and claimed Venezuela's crisis has been "fabricated by Washington" to justify intervention.
Venezuela is already experiencing mass hunger, and is likely to experience even greater difficulty importing food thanks to stepped-up US sanctions.
The U.S. has revoked visas for members of Venezuela's Constituent Assembly amid an ongoing push to ramp up pressure on Caracas, the special envoy for Venezuela said Thursday. They squeeze us by the neck and then make us beg for crumbs'.
"Take all that humanitarian aid and give it to the people of Cucuta, where there is a lot of need", Maduro said.
"We're going to open a humanitarian corridor and the doors to freedom", he told journalists. The Venezuelan military has barricaded a bridge connecting the two nations with a tanker and two cargo trailers in an apparent attempt to block the aid.
Guaido maintains that Maduro's second term as president is illegitimate, citing the May 2018 election that faced widespread global condemnation.
He claims his legitimacy from the constitution, but Maduro - labeled a dictator by the West and his Latin American neighbors - insists his re-election a year ago was constitutional.
No Venezuelan officials or opposition leaders participated in the meeting.
"Maduro has proven he will manipulate any calls for negotiations to his advantage and he has often used so-called dialogues as a way to play for time", he said.
Turning his ire on the Contact Group, Maduro aimed a message at the European Union.
The contact group issued a statement on Thursday, saying it would send a technical mission to Venezuela to ensure the delivery of humanitarian aid and would support a national vote.
He has dismissed Maduro as illegitimate over his reelection last May in polls branded a fraud by the US, EU and many Latin American countries.
Members of the South American country's security forces fear they or their families could be targeted by Maduro if they defect, so the USA would need to offer them something that could outweigh those concerns, said Eric Farnsworth, vice president of the Council of the Americas think tank in Washington.