McCain cancelled a news conference due to be held outside India's foreign ministry after India summoned a senior U.S. diplomat to the ministry over the spying report. (Agencies)
US and Indian officials gave differing explanations for the cancellation, but said it was not linked to the row.
India sought an assurance that any such surveillance would not recur.
"India has sought an explanation of the information contained in the press reports, and an assurance that such authorizations will not be acted upon by US government entities," the foreign ministry said in a statement.
Indo-US relations have been delicate for months, following a major spat over the treatment of an Indian diplomat who was arrested in New York in December, an incident that was widely blamed for the resignation of the US ambassador to New Delhi.
The Obama government has sought to revive ties since Modi's election in May, with an eye to ramping up bilateral trade and defence deals with India.
Modi was for years denied a visa for travel to the United States following religious riots while he was a state chief minister. He has responded positively to US advances and shown no resentment publicly.
McCain, whose Arizona constituency is host to some of Boeing and Raytheon's most important defence businesses, told the Senate last week that Washington should seek to help India's economic and military development. McCain and India's Foreign Minister Sushma Swaraj discussed taking forward bilateral relations, the situation in Afghanistan and Iraq, Indian foreign ministry spokesman Syed Akbaruddin told reporters. US Secretary of State John Kerry is also expected to visit India soon.
The United States does not currently have an ambassador in New Delhi and its most senior diplomat is the charge d'affaires.
Modi's Bharatiya Janata Party (BJP) was among a handful of political organizations a US court allowed the intelligence agency to spy on, according to a 2010 classified document leaked by former security contractor Edward Snowden and published by the Washington Post.
The other organizations included Lebanon's Hezbollah-allied group Amal, Egypt's Muslim Brotherhood, and the Pakistan Peoples Party, the leaked legal certification approved by US Foreign Intelligence Surveillance Court showed.
The ruling Bharatiya Janata Party (BJP) government led by Narendra Modi has not yet publicly commented on the snooping allegation. BJP leaders offered cautious remarks that the government would take appropriate action.
Akbaruddin said that if the snooping reports were true, it was ‘highly objectionable’.
The foreign ministry had voiced concerns a year ago about allegations that US agencies spied on Indian embassy in Washington, but critics say that the issue has largely been brushed under the carpet.
US officials acknowledged they have yet to respond and said they would do so, Akbaruddin said.
McCain cancelled a news conference due to be held outside India's foreign ministry after India summoned a senior U.S. diplomat to the ministry over the spying report.