The BJP government believes that "only one idea should run India," he said at a public rally organised by his party's southern ally, the DMK.
The meeting was attended by opposition leaders including TDP supremo and Andhra Pradesh Chief Minister N Chandrababu Naidu. UPA Chairperson Sonia Gandhi was also present.
Naidu, spearheading the effort to cobble up an anti-BJP front for the next year's Lok Sabha polls, hit out at the NDA government over what he called its "failure" in all areas.
He warned of what he described as a "danger" through "manipulation" of Electronic Voting Machines (EVMs), allegedly by the BJP, a charge put forth against the saffron party by its rivals lately.
Gandhi was addressing the rally after participating in an earlier event of the unveiling of late DMK President M Karunanidhi's statue at party headquarters Anna Arivalayam here.
Training his guns on the Modi government, Gandhi charged it with targeting institutions, besides the cultures of India.
Gandhi heaped praise on the Dravidian veteran, saying Karunanidhi defended the voice of people of Tamil Nadu, the institutions of this country and the southern state.
He said that today "we have a (Central) government that believes that only one idea should run India, a government that believes that the billions of voices in the country should not count. A government that does not respect the different languages and cultures of this country.
"I want to tell the people of Tamil Nadu, that in the memory of Karunanidhiji, and out of respect for your language, your culture, your tradition, everybody in India is going to get together, all voices in India are going to get together and are going to defeat the BJP in the next elections," he said.
The country will not allow 'destruction' of its institutions like the RBI, the Congress chief said.
"We are not going to allow the destruction of the idea of India. We are not going to allow the destruction of institutions -- the supreme Court, Reserve Bank of India, Election Commission of India," he said. "And we are going to stand together and do this."
Naidu also hit out at the Modi government.
"We all are victims now. Even Andhra Pradesh bifurcation Act provisions are not being implemented. They are not giving special status (to AP). In Tamil Nadu, there is a remote-controlled (AIADMK) government. Control is in Delhi. They are running the government. Federalism is totally destroyed and the CBI is being misused left and right," Naidu charged.
Former RBI Governor Urjit Patel resigned due to 'pressure', he alleged and claimed that a 'wrong affidavit' was filed by the Centre in the Supreme Court in the Rafale case.
Governors were being 'misused' while agriculture was in total distress, he said and criticised the government over demonetisation and NPAs in the banking sector.
"There is another danger-- EVM-tampering. I am cautioning the nation...today there is a danger through EVM. If they do manipulation through EVM, nobody can do anything."
Urging the voters of Tamil Nadu to pick the DMK-led combination in the 2019 polls, he exuded confidence the opposition coalition will win all 40 seats in Tamil Nadu and neighbouring Puducherry.
He also praised Karunanidhi.
Kerala Chief Minister Pinarayi Vijayan hailed Karunanidhi's focus "not merely on economic development" but on socioeconomic development as well.
As a chief minister, he was one of the "finest administrators," Vijayan said, and credited him with launching various initiatives in Tamil Nadu even before various Central governments did them, including equality for women in property.