"To all the presidents, I call on them to approve a meeting and through mutual dialogue, we can find a solution", said Maduro.
The U.S., the European Union, a number of Latin American countries and others around the globe have condemned the assembly, and the Vatican last week called for its suspension, all of which Maduro no doubt laughed off because now he basically controls the country.
He said he wanted the meeting، "if it can happen،" to be held when world leaders gather at the United Nations General Assembly in New York City on September 20. "Mister Donald Trump, here is my hand", he said.
The United States on July 31 took the unusual step of imposing sanctions on a head of state by targeting Maduro with measures freezing any U.S. assets he might have and barring Americans from doing business with him.
Trump recently imposed sanctions on Maduro, accusing him of undermining democracy.
The Constituent Assembly unanimously approved Maduro "as constitutional president of the Bolivarian Republic of Venezuela, head of state and government, commander in chief of the Bolivarian National Armed Forces", said the agreement read by the constituent member Aristobulo Isturiz during a special session on Thursday.
The opposition has criticized the assembly, filled with Maduro loyalists, as a power grab and attempt to install a "communist dictatorship".
The Trump administration also targeted Maduro himself, branding the Venezuelan president a "dictator" and freezing all of his assets subject to USA jurisdiction. "Today we have the National Constituent Assembly together، and I am here to recognize its plenipotentiary powers، sovereign، original، and magnificent to govern the destinies of the Republic،" Maduro said in his first appearance in the newly-elected legislative body on Thursday.
More than 125 people have died in violence since the opposition began a sustained wave of protests in April.
Analysts say that whether or not support for Maduro continues will depend on the evolution of the crisis.
The assembly, being called a "legislative superbody" by the global press, was his creation and won approval in a national election on Sunday that the opposition made the huge mistake of boycotting because they said it was illegitimate.
National Assembly president Julio Borges, leader of the country's opposition, has sent more than a dozen letters to leading global banks warning them of the risk to their reputations and bottom line if they throw a lifeline to Mr Maduro.