In the ad, Roy asked the regulator's top officials for a live 60-minute televised face-off.
The regulator accuses Sahara of raising billions of dollars from small investors through an outlawed financial scheme and failing to comply with a court order to refund the money.
An unlisted conglomerate best known as the lead sponsor of the Indian cricket team and more recently as a buyer of overseas luxury hotels, Sahara argues it has repaid most investors.
It says its total liability is less than the Rs 51.2 billion it had deposited with the regulator as the first repayment installment following the top court's ruling that the bonds it issued were illegal.
The money it raised from small investors, many of them poor villagers who don't have bank accounts, was to be invested in real estate and other projects, according to regulatory filings. Sahara's other businesses include media and retail.
The regulator declined to comment on the case, including Roy's challenge to the televised debate. Roy was not immediately available to be interviewed.
Like Sahara, Roy, 64, has long operated outside the mainstream of corporate India.
Based in Lucknow, the capital of India's most populous state Uttar Pradesh, Roy calls himself managing worker and chairman of Sahara and "chief guardian" of the world's biggest family, with nearly a million staff and agents. The conglomerate's full name is Sahara India Pariwar, which means family.
Sahara says the founders have taken an oath that neither they nor their family members can share the profit or assets of the company, although Roy lives in a sprawling gated complex of low white buildings and lawns called Sahara Shaher. His wife, Swapna, and two sons work for the company.
Sahara's website says it had assets with a market value of Rs 1.17 trillion as of April 2011, the most recently available figure on its website.
Its social initiatives include a mass wedding every year for 101 under-privileged couples, who each get gifts worth Rs 100000.
Rs 2000 and a scooter
While many of India's corporate titans are regulars on the World Economic Forum circuit, Roy, with a bushy moustache and often wearing a black waistcoat over a white shirt or a black Nehru jacket, is often photographed with celebrities such as cricket stars.
He does not feature on the Forbes list of 100 richest Indians, although he ranked 10th on India Today magazine's "power list" last year.
Unlike many of India's hereditary tycoons, Roy had humble business origins.
He started out in 1978 with a mechanical engineering diploma, Rs 2000 and a Lambretta scooter in Gorakhpur, Uttar Pradesh.
From modest roots, Sahara has pursued splashy deals.
In late 2010, it bought the Grosvenor House hotel in London and a year later acquired New York's Plaza Hotel, its two biggest overseas deals. In 2010 it looked into buying English Premier League soccer club Liverpool and the debt of film studio Metro-Goldwyn-Mayer, although neither deal materialised.
Roy's public profile is mostly linked to sport.
In 2011, Sahara paid $100 million for 42.5 percent of the Formula One racing team of liquor tycoon Vijay Mallya. A year earlier, it paid $370 million for the Pune Indian Premier League cricket franchise.
Roy gives infrequent interviews but is not publicity-shy. His website features photos of himself with Bill Clinton and Mother Teresa and the caption: "The world steps aside for the man who never stops."
During British Prime Minister David Cameron's recent visit to Mumbai, Roy was among local business leaders to meet him. Sahara sent a photo of the two of them to reporters.
Roy portrays himself as fiercely patriotic. Sahara's logo features the Indian tri-colour and the company frequently uses an image of Bharat Maa (Mother India) driving a chariot pulled by four snarling lions.
SEBI vs Sahara
He is also no stranger to controversy.
A dispute with Indian cricket's governing body early last year led Roy to briefly call-off Sahara's decade-long sponsorship of the national side.
But it is Sahara's financial business and the source of its funds that have long sparked curiosity in India. SEBI, in its uncharacteristically aggressive and public pursuit of Sahara, has questioned the authenticity of Sahara's investors.
"We challenge SEBI to find or prove even one fictitious investor," the company's ad this week said.
Last month, SEBI ordered a freeze on the assets of two Sahara companies as well as all accounts and properties in the names of Roy and three other directors of the two firms. It wants him arrested over what it says is Sahara's failure to comply with the court's refund order.
Sahara's defiant and rambling ad was the latest in its battle with the regulator.
"For absolutely no fault of ours at all, SEBI is continuously damaging Sahara's hard earned, clean image, reputation and goodwill earned in the last 34 years, by deliberately framing wrong orders and leaking them to press and electronic channels," Roy said in the ad.
The Supreme Court is expected to hear SEBI's request seeking Roy's arrest in early April.