The protests, which began in April, have left more than 100 people dead. The Venezuelan government continued its plans and shortly after the elections, Maduro was sanctioned.
On Saturday the nations of Mercosur, which includes Brazil and Argentina, issued a statement saying "the only acceptable means of promoting democracy are dialogue and diplomacy" and repudiating "violence and any option that implies the use of force".
The late July election of 545-member legislative superbody, called the constituent assembly and stacked with Maduro allies, drew global condemnation for usurping the authority of Venezuela's opposition-controlled congress.
The President of the United States of America said he was prepared to consider many options for addressing the unrest in Venezuela "including a possible military option, if necessary".
Assembly president and former Foreign Minister Delcy Rodriguez added in her tweets that "insults and aggressions" against Venezuelan President Nicolas Maduro would be rejected by the "anti-imperialist people of Venezuela".
Speaking to Journalists during an impromptu question and answer press conference, President Trump said that the people of Venezuela are suffering, and some are dying.
Trump said the crisis in Venezuela was one of the topics discussed during talks Friday in New Jersey with his secretary of state, Rex Tillerson, and U.N. Ambassador Nikki Haley.
Maduro expressed his desire to have a personal conversation with Trump, preferably when heads of state and government from around the world gather for the UN General Assembly in NY on September 20.More news: Charlottesville car crash suspect ID'd as 20-year-old Ohio man
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Ben Sasse, a senator from Nebraska and a member of the Senate Armed Service Committee, criticized the new position of the President on the Venezuelan crisis.
"Mr. Donald Trump, here is my hand", he said.
The US government has sanctioned more than 20 Venezuelan government officials in the last few weeks.
Maduro has come under fire by the opposition and my the major countries in the Americas for seeing over the establishment of a new assembly filled with loyalists given powers to override the legislature, controlled by the opposition since 2015.
Also Friday, the White House said Venezuela's Maduro had requested a phone call with Trump.
Following the meeting Arreaza is expected to deliver a government statement responding to Trump's remarks, which have been panned by government allies as a dramatic escalation of the country's political conflict.
In response, the White House said Mr Trump would gladly speak to his Venezuelan counterpart, when democracy had been restored in the country.