He also said that India was using Pakistan 'like a punching bag' in the aftermath of the strikes that killed 172 people.
"We don't kill people. Our mission is to spread the word of Islam and Allah's message on earth. And we are not Lashker-e-Toiba, we are Jamaatul Dawah," Makki told sources in an exclusive interview in his office here.
India, as well as US experts, say LeT is one of the principal suspects for last week's Mumbai terror strikes.
The US government's Excluded Parties List System lists the LeT as one of the alternate identities of the Jamaatul Dawah.
Makki also defended his chief, Hafiz Muhammad Saeed, against Indian charges of terrorist activities and demands for his extradition.
"They (the Indian government) are using Pakistan like a punching bag to divert attention from their failure to provide security to their own people. Strange! The government, which failed to keep the terrorists away, came to know just in half-an-hour after the attack that they were from Pakistan," Makki told sources.
He said that no one from the Pakistani government or any intelligence agency had contacted his organization since the Mumbai attacks and neither "have we gone underground as reported in the media".
"The Indian mindset has not changed. They have not forgiven us for dividing the subcontinent and are hoping against hope to unite what used to be Hindustan," he said, while urging the Indian leadership to adopt a policy of coexistence.
Wearing an off-white shalwar kameez and black waistcoat, the grey bearded Makki replied to questions in the manner of a shrewd diplomat.
Unlike traditional religious leaders, he wears his hair short and keeps it uncovered.
Makki said that in the last four years, more than 5,000 people had been killed in terrorist attacks in India. "Who killed them, who killed (Mahatma) Gandhi, who killed Indira (Gandhi), Rajiv (Gandhi) and many other leaders," he asked when questioned why the LeT was being blamed for the Mumbai attacks.
"Write it down - that an independent inquiry by India's own agencies will prove that India's own people were behind the attacks," he maintained.
When asked if the LeT was still operating in Indian Kashmir, Makki was quick to respond that his organization "whatsoever has no relations with LeT except for providing them moral support".
"I challenge you to bring me a single paper of LeT which carries signature of Hafiz Muhammad Saeed or any of our workers.
Yes, we used to provide moral support to LeT but all their offices in Pakistan have been closed since the 9/11 incident," said Makki, who was a lecturer at Lahore's prestigious University of Technology and later at Makkah University in Saudi Arabia.
"What's wrong in supporting Kashmiri organizations when America has supported East Timor, Israel, Taiwan and recently Georgia and India has supported Maoists, Tamil Tigers, Mukti Bahni, and separatists in Pakistan and many other countries," said Makki, who added this title after staying in Makkah for about 14 years.
He said the LeT was one of several Kashmiri organizations that had their offices in Pakistan but now, "none of them has any office in Pakistan".
He was also not sure if the LeT was still operating in Indian Kashmir. "We haven't heard from them for long and I believe if they are still there (in Kashmir), they must have been reduced to a small organization."
Makki laughed away media reports that India may attack his organization's headquarters near Lahore, saying "any attack on our office will be attack on Pakistan".
He was of the view that American hegemonistic designs and presence in the region had "encouraged" India to issue "irresponsible" statements against its neighbours.
"America has never created problems with its immediate neighbors as it wants to keep the area peaceful but India, despite its huge economy and size, has always been at war with all its neighbors.
"It is strange that India is creating problems for its own people and the people of the region," Makki said, adding: "Are we living in a fools' paradise?"
Urging the Indian leadership to "be responsible for ensuring peace in the region", he lamented that the country's two major alliances had proved their "inability" to rule the world's largest democracy.
"They (the Congress and the BJP) are power hungry and have proved that they can go to any extent to win elections. For god's sake, be responsible and set your own house in order. Don't try to crush the minorities otherwise you may face more terrorism, not from outside but from within, from your own people," Makki maintained.
He said that India was out to harm Pakistan as its leadership had not yet accepted the division of the subcontinent.
"Their first attempt was to snatch Kashmir, the second to separate East Pakistan (now Bangladesh) and now they are blocking Pakistan's waters, not only from India but from Afghanistan as well," he said, adding that India has funded a huge dam in Afghanistan that is being built on the Kabul river.
With the Kishan Ganga dam in India and the dam in Afghanistan, Pakistan would face a severe water shortage leading to drought and "another war between the two countries", Makki warned.