The mounting political pressure comes after one of the worst and longest blackouts in recent memory in Venezuela.
The outage had left most of the country in disarray, crippling day-to-day functioning of hospitals and other public services, according to local press reports.
However, President Nicolas Maduro's government has not moved directly against Guaido since he returned to Venezuela from a Latin American tour Monday.
Engineers restored power in some places after electricity and communications shut down nationwide Thursday evening, but outages persisted in many areas where people are already beset by hyperinflation as well as shortages of food and medicine.
However, he said more than 90 per cent of generators that were part of a government contingency plan successfully provided power to Venezuelan hospitals, ensuring there were no major problems for seriously ill patients.
The power flickered on and off in parts of Caracas on Saturday morning. The move is supported by the USA and about 50 other countries.
At the pro-government rally, people danced and waved flags on what organizers labeled a "day of anti-imperialism" in a show of defiance toward the United States, which has imposed oil sanctions on Venezuela in an attempt to oust Maduro.
As night fell Saturday, much of the country was still without power. The Information Ministry did not reply to a request for comment. The blackouts heightened tension between the bitterly divided factions, which accused each other of being responsible for the collapse of the power grid.
"We have a complete lack of services", says another resident.
"They think they can wear us down, but there's no way they can contain a population that has chose to end the usurpation", added the leader of the opposition-controlled legislature, who is recognised as Venezuela's interim president by more than 50 countries.
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"They think they can scare us but they will get a surprise form the people in the street", Guaido tweeted.
Police were out in force on the road in Caracas where Saturday's opposition march was planned.
For six weeks now, Venezuelans have had their allegiances tested by two men who claim to be the president.
Guaido and US officials scoff at the notion, attributing the blackout to alleged corruption and mismanagement under Maduro's government.
Opposition activists last month attempted to bring food into the country via Colombia but the aid convoys were halted at the border and two aid trucks went up in flames.
The U.N. doctrine sometimes referred to as R2P was created to prevent mass killings such as those of Rwanda and Bosnia and places the onus on the worldwide community to protect populations from crimes against humanity and ethnic cleansing.
Mr Maduro took over the presidency when his late mentor Hugo Chavez died in 2013. He said the "macabre strategy" to make Venezuelans desperate and turn them against each other would fail.
Guaido blamed the blackout on government corruption and mismanagement while the Socialist Party claimed it was part of a USA -sponsored plot to force Maduro from power.
This story has not been edited by Firstpost staff and is generated by auto-feed.