Supreme court order
The summons follows a supreme court order last year to probe a complaint filed by Zakia Jafri, widow of Ehsan Jafri, a member of parliament, who was killed in the riots on February 28, 2002.
Reports say Jafri, a former member of parliament from the Congress party, was hacked to death and burnt by Hindu extremists who stormed the Gulbarg Society, a residential complex housing Muslim families in Ahmedabad, Gujarat's largest city.
Previous investigations into the riots commissioned by the Gujarat government have absolved the state police and government of collusion or intentionally failing to stop the riots.
However, last March, Maya Kodnani, Gujarat's women and child welfare minister, was arrested on charges of leading a mob that killed more than 100 people during the riots, making her the highest-ranking state official to be detained.
The violence broke out after 59 Hindu pilgrims were burnt alive after train compartments in which they were travelling were torched. A Muslim group was blamed for the incident, but an inquiry later said the fire was accidental.
Modi is a prominent member of the BJP and has been touted as a future prime minister.