The business community, fearing future power shortages, mostly favours building the plant, which is one-third complete.
The groups - which helped vote in the government because of its promise to scrap the plant - plan to hold a series of protest demonstrations.
An official in Kungliao a town, sited near the plant, said people were disgusted that politicians had betrayed their consciences and abandoned their principles.
The government caved in to pressure from the opposition-dominated parliament and signed an agreement on Tuesday to continue the project in order to break a political impasse.
Premier Chang Chun-hsiung said the decision was a painful.
"If we allow this standoff to continue, it will cause economic and social chaos."
The issue provoked a bitter political feud that has left parliament deadlocked and damaged the economy, contributing to a 40% drop in share values on the Taipei stock exchange.
The row began in October, when the government - without consulting parliament - announced it would scrap the partially-built $5.5bn plant for financial and environmental reasons.
Economic impact
Correspondents say the dispute had overshadowed all other government business.
The business community, fearing future power shortages, mostly favours building the plant, which is one-third complete.
But environmentalists say Taiwan - which already has three atomic power plants - lacks the ability to process nuclear waste and deal with accidents.
Mr Chang said the cabinet would restore the budget for the plant and resume construction "with the highest safety standards". He signed a draft compromise on the project with parliament speaker Wang Jin-pyng on Tuesday.
Analysts say the government's climbdown will also anger its own supporters in the Democratic Progressive Party (DPP), many of whom have a hardline anti-nuclear stand.
Scrapping the plant was a campaign promise made by the party which won the election last year.
Fight not over
Some legislators in the DPP have said the fight is far from over, threatening to shelve the project again if the DPP becomes the biggest party in parliament after elections at the end of the year.
The BBC's Taiwan correspondent, Damien Grammaticas, says it could lead to resignations of senior figures and could harm the party's chances in this year's legislative elections.
The project was pushed through in 1986 by the then-ruling Kuomintang, now the main opposition party, despite years of objections from environmentalists and residents.
The KMT was outraged that it had not been consulted about the scrapping of the project.
The island's highest court then ruled the prime minister must win the support of parliament to proceed with his policy, and ordered the two sides to negotiate a settlement.