Supporters of the Maduro government are holding counter-protests.
The opposition marches were called by the National Assembly to mark the anniversary of the 1958 coup which overthrew dictator Marcos Perez Jimenez.
Ahead of the opposition marches, the Venezuelan bishops' conference called them "a sign of hope, something new that is beginning to be generated in our country: necessary changes for the integral human development of each person and of all persons, but always in democracy and in accord with the National Constitution."
"These marches are not the end of the road, but a sign of the future in process which we must construct among us all, without exception," the bishops said in a statement titled "23 January 1958: A historic milestone for Venezuelan democracy."
The bishops called the 1958 coup "an inspiring sign of the triumph of social rationality before the abuse of power; of the unity of the people who were weak before the dismantling of a regime of abuses, of corruption, and of repression, which concealed within itself all the evils which an authoritarian government can have."
Since then, the Venezuelan republic developed a "democratic conscience", which valued the separation of powers, peaceful transitions of government, and decentralization, the bishops said.
"Lamentably, the deterioration of the democratic life by factors known to all opened the doors to the introduction of a government regime in which many placed their hopes, but which, in the end, has been contrary to the principles of social ethics and to respect for human dignity."
They said the Jan. 23 marches remember "that event which was significant in the struggle of civilization before barbarism. We do this remaining aware of the suffering to which the Venezuelan people have been subjected by government action."
The bishops also said that "the majority of the people ask for a change of direction which passes through a period of transition until new national authorities are elected."
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On Jan. 9, the bishops had said Maduro's claim to be initiating a new term "opens the door to the nonrecognition of the government, since it lacks democratic support in justice and law."
A Jan. 21 rebellion by 27 members of the National Guard in Caracas was quickly suppressed.
Venezuela's socialist government is widely blamed for the country's crisis. Since 2003, price controls on some 160 products, including cooking oil, soap and flour, have meant that while they are affordable, they fly off store shelves only to be resold on the black market at much higher rates.
Poor economic policies, including strict price controls, coupled with high inflation rates, have resulted in a severe lack of basic necessities such as toilet paper, milk, flour, diapers and medicines.
An estimated 3 million people have fled the country since 2014.
Inflation in Venezuela in 2018 was estimated by the National Assembly at 1.3 million percent.