Of the 10,787 samples, 736 were positive for the UK variety, 34 for the South African variety and one exception for the Brazilian variety.
The report comes amid a recent spate of Covid cases in India.
But the government said there was no communication between the speaker in the cases and in these cases.
India reported 47,262 cases and 275 deaths on Wednesday - the largest daily increase this year.
The Indian SARS-CoV-2 Consortium on Genomics (INSACOG), a group of 10 national laboratories under the Indian Ministry of Health, is conducting a series of samples. Genomic sequencing is a process of testing to draw all the genetic code - in this case, the virus.
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The genetic code of the virus serves as its instruction manual. Mutations of viruses are common but most of them are not significant and do not cause any other changes in their ability to transmit or cause major infections. But other genetic mutations, such as those in different parts of the UK or South Africa, can make the virus more infectious and in some cases even more deadly.
Double mutation, explains pathologist Shahid Jameel, "is a genetic mutation that results in a single virus".
"Double mutations in key areas of viral spike protein can increase these risks and allow the virus to escape the immune system and make it more susceptible to infection," he adds.
Spike protein is the part of the virus that it uses to enter human cells.
The government said the analysis of samples collected in India's western province of Maharashtra shows "an increase in the proportion of samples and changes in E484Q and L452R" compared to December last year.
"Changes such as these provide an immune response and an increase in infection," the Department of Health said in a statement.
Dr. Jameel added that "there may be a different genealogy developing in India with the L452R and E484Q mutations".
However, the government has denied that inflation is linked to reforms.
"While the VOCs [worrying variety] and double-digit innovation have been found in India, these have not been available in sufficient quantities to build direct relationships or explain the rapid increase in cases in other provinces."
The latest report comes after a number of experts called on the government to intensify its genetic testing efforts.
"We must always be vigilant and ensure that there is no further concern for the people. The fact that this is not happening now does not mean that it will not happen in the future.
India became the fifth country in the world to have a generic coronavirus sequence after separating it from some of the first cases the country recorded in January last year.
With more than 11.7 million cases and 160,000 deaths later, efforts are underway to identify changes.
The latest outbreak - which began this month - comes at a time when some experts call India's 'critical phase' - the health care system is tired of a year-long battle against coronavirus.
Countries have begun to re-introduce restrictions, including timeframes and periodic closures, to control the spread of the virus.
Two major cities, the capital Delhi and Mumbai, have also ordered rapid surveillance at airports, train stations, and crowded places such as supermarkets.