"What we have said is that we expect a response and an assurance that this won't happen again," a foreign ministry source told AFP on condition of anonymity.
A new classified document made public by the Washington Post on Monday showed that Prime Minister Narendra Modi's Bharatiya Janata Party (BJP) was among authorised targets for the NSA in 2010 while it was India's main opposition.
India has complained to the United States on two previous occasions, in July and November 2013, over other revelations including the disclosure that its UN mission in New York and its Washington embassy were snooped on.
Both times Washington has said it would look into what it can share about its espionage programme but failed to offer any details, the source said.
"We have said that we would like a response, which we haven't received," he said.
The new incident comes ahead of a visit to New Delhi by US Secretary of State John Kerry, who is expected to meet Modi and other government members in the next few months.
The Indian PM, whose party swept to power in May with the first majority in 30 years, will travel to the United States in September for the UN General Assembly and his first meeting with President Barack Obama.
Senator John McCain arrived on Monday, the first high-ranking US politician in India since the change of government.
He met Foreign Minister Sushma Swaraj but then cancelled a scheduled interaction with the press as news of the latest diplomatic row played out on Indian news channels.
The BJP was listed among six foreign political parties along with Egypt's Islamist movement the Muslim Brotherhood and the Pakistan Peoples Party on which the NSA was given permission to carry out surveillance in 2010, says the document published by the Washington Post.
It was supplied by fugitive US intelligence worker Edward Snowden.
"We have taken note of these reports of illegal spying by a foreign country's agency on the BJP and it is certainly not good," the party's vice president and senior spokesman Mukhtar Abbas Naqvi told AFP.
"Our government is already looking into it and will act in accordance with procedure."
The US embassy in New Delhi is currently between ambassadors, meaning acting ambassador Kathleen Stephens is its most senior diplomat.
State Department spokeswoman Jen Psaki confirmed that diplomats from the American embassy had met with their Indian counterparts following the revelations, but refused to detail what she said were "private conversations."
Relations are still recovering from a damaging dispute in December about the arrest of an Indian diplomat in New York, who was charged with visa fraud over the employment of a domestic servant.
The detention provoked a furious reaction from India and raised more doubts over a troubled alliance which Obama hoped in 2009 could become "one of the defining partnerships of the 21st century".
The US is keen to build personal relations with Modi, having been the last country to lift a decade-long boycott of the Hindu nationalist over religious riots which occurred while he was running his home state of Gujarat in 2002.
US ambassador to India Nancy Powell resigned in April, six weeks after she met Modi for the first time amid criticism that Washington had been too slow to embrace the man widely tipped to win this year's election.