The project would mark another step in the country's ambitious space programme, which placed a probe on the moon three years ago and envisages its first manned mission in 2016.
"Our spaceship will go near Mars and collect important scientific information," Singh said in his annual Independence Day address, heralding the plan as "a huge step for us in the area of science and technology".
The Indian Space Research Organisation (ISRO) is expected to launch the unmanned orbiter as early as November next year, the Press Trust of India news agency reported earlier this month.
According to one ISRO official, the cost of the mission has been estimated at four to five billion rupees ($70-90 million).
The United States, Russia, Europe, Japan and China have all sent missions to Mars.
The US robot Curiosity is currently on the surface of the "Red Planet" after landing last week to hunt for soil-based signs of life and send back data for a future human mission.
India's planned Mars mission comes as the government has been under pressure over issues such as massive power shortages and the nation's poor transport infrastructure.
Blackouts on two consecutive days this month knocked out power in vast swathes of the country.
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