The Ministry of Health and Family Welfare said senior doctors from its Central TB Division and the World Health Organization had been sent to the city to meet public health officials to "ascertain the facts" of the cases.
Doctors from the private Hinduja Hospital in Mumbai said in a research paper published last month that they had identified four patients with TB who failed to respond to any of the standard drugs used to treat the disease.
This suggested they were untreatable, the researchers said.
Those cases -- and eight others reported later -- have prompted officials in Mumbai to consider setting up an isolation facility to prevent the spread of the deadly strain.
But the government in New Delhi has disputed the report's findings, claiming that the hospital was not an accredited centre to diagnose extensively drug-resistant TB (XDR-TB) or totally drug-resistant TB (TDR-TB).
In addition, TDR-TB was not a term currently recognised by the WHO, it added in an emailed statement.
Tuberculosis is an airborne disease that primarily affects the lungs. It is spread in a similar way to the common cold when an infected person coughs or sneezes, spreading TB microbes or bacilli.
More than two billion people -- or a third of the world's population -- are infected with TB bacilli, according to the WHO. One in 10 people will subsequently fall ill with active TB.
An infected person who is not properly treated can infected 10 to 20 people a year.
Tuberculosis is endemic in India, with widespread poverty, lack of adequate healthcare and the stigma of the disease that prevents people seeking treatment all cited as contributory factors to its spread.
Nearly 1,000 people die from TB every day -- the equivalent of two deaths every three minutes.
Report author Zarir Udwadia, a consultant chest physician at Hinduja Hospital, criticised the government for disputing its findings.
"The patients have been given all these drugs or almost all of them. Their parameters are matching the resistance profiles," he told AFP.
The first cases of totally drug-resistant TB were identified in Italy and Iran in 2007 and 2009 and the Indian cases are the first since then, the New Scientist magazine said in a report last week.
Udwadia said it was only a matter of time before it appeared in India due to inadequacies in the state TB treatment programme.
Currently, less than one percent of people requiring more expensive second-line drugs for multidrug-resistant TB receive them, he added.
"TB remains a disease of poverty," he said. "I don't think this form is going to be more deadly or more lethal. There are a few patients and reports creeping out of the woodwork from other parts of the country."
"But we have to have legislation to make sure that treatment is given by specific doctors who know what they're doing and the government programme has to reach larger numbers of people with MDR-TB."