In a written apology to Kalam and the Indian government, the US said, "Appropriate procedure for expedited screening of dignitaries had not been followed". (US says sorry: Read full statement here)
They also said that US was actively working to prevent such incidents from occurring in the future.
India has strongly objected to the incident. External Affairs Minister SM Krishna had asked India's envoy to Washington, Nirupama Rao, to take up the issue at the highest level. (Read: Indian government's statement on Kalam screening)
"This is unacceptable and is being taken very seriously," Mr Krishna had said.
Mr Krishna had also asked Ms Rao to tell Americans that India may reciprocate.
80-year-old Dr Kalam was in the United States in September to attend a series of events and the incident took place while he was returning home from New York on September 29.
Sources said after Dr Kalam had taken his seat in the aircraft, officials of the John F Kennedy (JFK) Airport came inside and said they wanted to check the former President once again, which was strongly protested by Air India authorities.
However, the airport authorities were adamant about searching the passengers again, the sources said, adding Dr Kalam did not protest.
"Later, they took away his shoes and jacket much to the dissatisfaction of the Air India authorities. However, they returned them later," the sources said.
A detailed report on the incident was prepared by Air India's Director (Security) S Mathur and sent to the Civil Aviation Ministry which in turn forwarded it to the External Affairs Ministry in October.
"As the incident happened on the American soil, I have been informed that US security agencies are investigating it now. Such incidents should not happen," Civil Aviation Secretary Nasim Zaidi told PTI.
An External Affairs Ministry spokesperson said officials of both the countries were working on ways to avoid recurrence of such incidents in future, including preparing a common list of VIPs.
This is the second time Dr Kalam has been frisked by an American airline. On April 21, 2009, the former President was frisked by the staff of Continental Airlines at Delhi airport. The incident had led to a huge uproar in India with a debate being raised in Parliament. The airline and the US government had later apologised to Dr Kalam following India's protest.
Other senior Indian officials too have not been spared by US authorities in the past. In December last year, Indian Ambassador to the US Meera Shankar, was subjected to a pat down because she was wearing a sari. This was despite the fact that the US authorities were aware of her diplomatic status. And days later India's envoy to the UN Hardeep Puri was subjected to similar checks. But as Kalam is concerned, US authorities had breached protocol when it frisked the former President. Current protocol exempts the President and former Presidents from airport security checks.
CPI M General Secretary Prakash Karat echoed the general sense of outrage in India over the frisking of Kalam but went one step further. He demanded that India reciprocate in kind to the US. Karat recounted how other countries like Brazil were already doing this to the Americans.
"I remember a time when I went to Brazil, years ago, I was quite surprised, there was a separate queue for US citizens, they were finger-printed and photographed because Brazilian citizens were being finger-printed. None of us were but American citizens were because they were doing it to Brazilians in United States, so institute the same here,'' Karat said.
(With PTI inputs)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.