People hold portraits of opposition leader Antonio Ledezma during a news conference at the Venezuelan coalition of opposition parties (MUD) headquarters in Caracas, Venezuela August 1, 2017.
She also ordered prosecutors to investigate the allegations of election tampering.
Maduro's government plans to install a new national assembly, which will draft a new national constitution to give the president sweeping new powers.
The body's 545 delegates were expected to be installed at the legislative palace in a room just metres from the chamber where the opposition-controlled National Assembly meets.
But former foreign minister Delcy Rodriguez, who will be the new assembly's president, said in an opening speech: "There is no humanitarian crisis here".
Electronic voting technology firm Smartmatic, which created the voting system used by Venezuela since 2004, said the turnout figures had been tampered with.
"The only way they'll get us out of here is by killing us", declared Freddy Guevara, the National Assembly's first vice president. "We thank the people of Venezuela and the worldwide community for their concern and solidarity".
"The Holy See appeals firmly to all of society to avoid all forms of violence and invites, in particular, the security forces to refrain from excessive and disproportionate use of force", the Vatican said.More news: With live-fire drill, China warns India not to test Beijing
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Over the last four months, Caracas has been rocked by violent protests which have resulted in the deaths of 125 people, and more than 5,000 people have been detained by security forces.
The Vatican statement called for a negotiated solution following the same guidelines the Vatican set out a year ago when it brokered talks between the government and the opposition which later broke down.
It called in a statement on "all political actors, and in particular the government, to ensure full respect for human rights and fundamental freedoms and the existing Constitution".
"There has been a gradual erosion of democratic practise and this is a significant line that has been crossed", said Michael Shifter, president of the Washington-based think tank Inter-American Dialogue.
The Constituent Assembly marks a new stage in Venezuela's rule.
Livingston, a longtime supporter of Venezuela's Bolivarian Revolution, also argued that the crisis is due, in part, to the government not heeding his advice on infrastructure investment, which he claims could have reduced the state's reliance on oil.
Opposition lawmakers have pledged to remain in power no matter what action is taken by the constitutional assembly, raising the possibility of two governing bodies operating side by side, with neither recognizing the other.