The scheme was launched in Delhi on August 20 by UPA chairperson Sonia Gandhi.
At the launch of the scheme, Ms Dikshit had said food grains under the programme would be distributed from September 1.
The Chief Minister distributed the food grains to the beneficiaries at Lakshmibai Nagar, South Kidwai Nagar, Krishna Menon Marg and Copernicus Marg in central Delhi.
All the areas where Ms Dikshit distributed food grains fall under New Delhi constituency which she represents.
A number of Congress MLAs also distributed food grains in their respective constituencies.
Ms Dikshit said Delhi government will provide benefits under the scheme to 73.5 lakh people in the city out of the total population of 1.68 crore.
In the first phase, the government will distribute food grains to 32 lakh beneficiaries.
She said the process of reaching out to the remaining 41 lakh persons has already started.
"My government is committed to cover all 73 lakh persons under the Food Security Programme by January next year as the parameters for identification of the beneficiaries have been meticulously finalised.
"The scheme would go a long way in overcoming hunger and alleviation of poverty across the country apart from enhancing the status of women," Ms Dikshit said, addressing a gathering at Laksmibai Nagar.