Maduro signed an executive order that will form a "Constituent National Assembly" -- a body that could make those changes. It also would allow for the reshaping of the current legislative body, as well as redefine the President's executive powers.
While Maduro provided few details, he said that the new body would contain "some 500 constituents," who will be elected during a "direct and secret" vote.
"We must modify this state, especially the rotten National Assembly that's currently there," Maduro said. The body is controlled by the opposition.
Maduro announced his plans earlier while speaking to a large crowd of government supporters who had gathered for May Day celebrations.
While the atmosphere at Maduro's speech was one of excitement and celebration, elsewhere in Caracas opposition protesters were being met with tear gas and water cannons. Opposition protesters have been out on the streets since the beginning of April, calling for elections.
The elected constituents would represent all sectors of the Venezuelan society, including workers, youth, women, peasants, those who receive pensions, and indigenous people, among others. He said some 200-250 would be elected via direct vote.
He emphasized that those elected to the body would be chosen by the people -- and not by the political parties.
Leonel Alfonso Ferrer, a Venezuelan constitutional attorney, tells CNN en Espanol that, in the short term, nothing changes.
"The country will continue to be ruled by the political institutions that it currently has. The presidency will remain in the hands of Nicolas Maduro. The National Assembly Venezuelan will still be controlled by the opposition, and so on. When the national constituent assembly is in place and its members are chosen, that assembly, as an original constituent power, will have powers that are above the Constitution and will eventually be able to rewrite the Constitution and transform the state [...] as well as remove the president, the National Assembly and the Supreme Court."
The last time Venezuela called for a Constituent National Assembly was in 1999, when then-President Hugo Chavez drew up the country's current Constitution. Maduro said it would be a special chapter in the country's history, a move to defeat the "facist coup" and to promote peace and stability in the country.
The opposition has called this move by Maduro a "self-coup." Opposition leader Henrique Capriles said Maduro was "killing the Venezuelan Constitution."
Julio Borges, leader of the National Assembly, echoed Capriles's statement, calling it a coup against the Constitution and democracy. He called it a fraud.
"What has happened today, and I say without exaggerating or trying to be dramatic, is the greatest coup in the history of Venezuela. It's Nicolas Maduro dissolving democracy and dissolving our republic. Faced with this, the Democratic Unity Party and the members of the National Assembly call on the Venezuelan people to rebel and refuse to accept this coup."
Venezuela has been rocked by violent protests
in recent weeks as opposition leaders have faced off with Maduro and his supporters. Venezuela's attorney general said that at least 29 people have been killed since the protests erupted at the beginning of April. This number includes many cases unrelated to the political protests, including incidents of looting, CNN has found.
Anti-government protesters want Maduro to step down and new elections be held. The government has repeatedly blocked any attempts to oust Maduro from power by a referendum vote. It has also delayed local and state elections.
The last vote held in Venezuela, the parliamentary election of 2015
, gave the opposition a majority. Critics say elections have been delayed because Maduro is afraid of the outcome.
The political turmoil comes against the backdrop of a worsening economic crisis
. Despite having the largest proven oil reserves in the world, Venezuela is fast running out of cash
, and its people have struggled for years with food and medical shortages, coupled with skyrocketing prices.