Officials said the allegations were unacceptable and sought assurances from the US that it would not happen again.
In opposition then, the BJP came to power in May.
In a new document supplied by Mr Snowden and published by The Washington Post on Monday, the BJP is named along with Lebanon’s Amal, Egypt’s Muslim Brotherhood and the Pakistan People’s Party for being among authorised targets for the NSA in 2010.
“What we have said is that we expect a response and an assurance that this won’t happen again,” news agency AFP quoted an unnamed foreign ministry official as saying on Wednesday.
This is the third time India has taken up the issue of spying with the US – last year, Delhi complained to the US on two other occasions over similar revelations, including the disclosure that its UN mission in New York and its Washington embassy were snooped on.
Both times Washington said it would look into the complaint, but Indian officials said nothing came of it.
Delhi and Washington have strong security and trade ties, but relations have deteriorated in recent months after a row over the arrest and brief jailing on an Indian diplomat in New York on a visa fraud charge.
Correspondents say the latest revelations may put a strain on Delhi-Washington ties at a time when the two countries have been trying to improve relations amid expectations that Prime Minister Narendra Modi would visit the US in September to attend the UN General Assembly and also meet President Barack Obama.