Parliament speaker Henry Ramos Allup said proposals would be presented in a matter of days – rather than months.
A day earlier, Nicolas Maduro was given backing by the Supreme Court for a declaration of economic emergency, giving him greater powers.
The country is facing a shortage of many staple goods and rampant inflation.
Venezuela’s economy is heavily dependent on oil exports and has suffered substantially in the past year given the sharp fall in crude oil prices in international markets.
Energy rationing has been imposed, blamed by government ministers on critically low water levels caused by drought at 18 of the country’s hydro-electric dams.
The National Assembly speaker and other opposition leaders had previously announced they planned to challenge Nicolas Maduro in six months’ time.
However, Henry Ramos Allup now says Venezuela cannot afford to wait.
“Nobody doubts now that that six-month timeframe is too long,” he said.
“It is not we who impose the timing, it is the needs of the country.”
“In the next few days we will have to present a concrete proposal for the departure of that national disgrace that is the government,” he told a news conference.
Henry Ramos Allup called on President Nicolas Maduro to revoke the decree on emergency measures.
He also attacked the Supreme Court over the decree, saying if what it “has done is not a coup, I don’t know what to call it”.
Most if not all Supreme Court judges have been appointed either by Nicolas Maduro or his predecessor, the late Hugo Chavez. It rarely rules against the government.
Nicolas Maduro defended the court’s ruling and said the measures were necessary to deal with the crisis.
“This decision was taken by the highest court of the country, in accordance with the constitution,” the president said.
Nicolas Maduro’s decree was issued on January 14. It is valid for 60 days and it can be renewed by the president.
The government says businessmen linked to the opposition have been hiding basic staples such as flour, sugar and toilet paper as part of a strategy to undermine the economy and oust Nicolas Maduro’s democratically elected government.
He was elected in April 2013 to a six-year term, replacing Hugo Chavez, who died of cancer after 14 years in office.
The Venezuelan constitution says that a referendum to replace the president can be called any time after the first three years of his term, which will be in April 2016.
Four million signatures are needed to trigger a recall referendum.
The governing Socialist Party suffered a heavy defeat in December’s legislative election. It lost control of the National Assembly for the first time in 16 years.
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