The airport authority runs Sri Lanka's only international airport in Katunayake, which is north of the capital, Colombo.
The delegation had then been taken by a Sri Lanka Air Force aircraft to the proposed airport development site in Weerawila, in southern Sri Lanka's Hambantota district.
"The proposed airport site is 15kms away from Hambanota, a fast developing city, in the southern province of Sri Lanka which is about 300 kilometres from Colombo and is also the political constituency of the President," CIAL managing director S Bharath said in a statement.
Sri Lanka is also developing a port in Hambantota with Chinese funding.
CIAL is 26 percent owned by the Kerala state government and central government and had contributed capital from Indian expatriates and is showcased as a model for bringing private capital into airport infrastructure.
CIAL said President Rajapakse was "highly impressed" by its capabilities as an airport developer and consultant.
The Indian delegation has had a second round of talks with Ports minister Rajapakse. A Sri Lankan delegation is to make a follow up visit to India to take the discussions forward, CIAL said..