Non-governmental organisations fear a victory for Novartis could set a precedent for other pharmaceutical companies seeking patent protection for essential medicines.
These would include antiretroviral Aids drugs, currently made cheaply in places like India. India's patent law, which came into effect on January 1, 2005, allows patents for products that represent new inventions after 1995, the year India joined the World Trade Organisation, or for an updated drug that shows greater efficacy.
Novartis insists that its improved drug is more easily absorbed by the body.
But Indian drug companies and aid groups say Gleevec is a new form of an old drug invented before 1995.
Several Indian pharmaceutical companies already make generic copies of Gleevec, but sell it at a tenth of the $2,600 price for a monthly dose charged by the Swiss company.
Unni Karunakara of Medecins San Frontieres, the international aid group, said: "Novartis is trying to shut down the pharmacy of the developing world."
The group, along with Oxfam, has submitted a 250,000-signature petition to Novartis asking it to drop its case.
Novartis has defended its position and said it will offer its leukaemia drug for free to patients who cannot afford it even if it wins the case.
Paul Herrling, head of Novartis's corporate research, said: "We don't fight for Gleevec, we fight for the principle."
Indian companies make a host of other generic drugs, available at a fraction of the price of branded medicine and used throughout the developing world.