"Party that comes second has no right to form government," he tweeted this morning.
The response comes a day after the BJP announced that it is all set to form government in Goa and Manipur, claiming it has support of majority legislators.
Manohar Parrikar, who will take oath as Goa Chief Minister tomorrow evening, met with Governor Mridula Sinha on Sunday and was invited to form the government. Mr Parrikar today said that he has resigned as union Defence Minister.
Accusing the BJP of "murdering the democracy", Congress' Priyanka Chaturvedi said, "Mr Parrikar did not even contest election...no one knows if he is popular among the people of Goa... this is murder of democracy in broad day light."
Rejecting the allegation, BJP leader GVL Narsimha Rao said, "We secured 4 per cent more popular votes than the Congress, we also have legislative majority to form government... they (Congress) don't have."
Goa has 40 seats of which the Congress won 17, falling short of the magic number 21. The BJP, which is the incumbent, won 13. Many regional parties have extended their support to the BJP in Goa on a condition - Mr Parrikar will lead the government.
"We have letters of 30 MLAs and the 31st will send a letter to the Governor," said Himanta Biswa Sarma, who had joined the BJP from the Congress.
G Gaikhangam, Deputy Chief Minister of Manipur, said: "The Chief Minister (Okram Ibobi) has staked claims (to form government)... we are the single largest party we should be invited first to take a floor test."
Mr Chidambaram comment comes a day after he acknowledged PM Narendra Modi as "the most dominant political leader" in the country.
PM Modi exhaustive campaign in UP won the BJP the strongest result for any party since 1977 in India's politically most-strategic state. The BJP won all but 76 of the state's 403 seats.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.