Kumar, who is currently in the island for the 3rd Asian Region conference of the Commonwealth Parliamentary Association, said in an interaction with Indian journalists here: "What we are committed (to), we are doing it".
Asked whether India is happy with the pace of resettlement and rehabilitation in Sri Lanka's Tamil-dominated areas after three decades of a bloody civil war, she said "we should be happy how much of commitment (sic)".
India has pledged 50,000 houses for the internally displaced persons in Sri Lanka, in addition to developing infrastructure facilities.
"We should not slow down," Kumar said, referring to Indian government's commitments for rehabilitation work in a post-war Sri Lanka and emphasised "that has not happened".
On the recent incident in which two Indian fishermen were killed allegedly by the Sri Lanka navy, Kumar said Sri Lankan authorities need to throughly investigate the incidents and take suitable action.
The speaker also said that she and her Sri Lankan counterpart Chamal Rajapksha discussed "more frequent parliamentary exchanges" between the two countries.
She met senior Sri Lankan government officials along the sidelines of the CPA conference, including President Mahinda Rajapaksa and Prime Minister D M Jayaratne.
Kumar said that she discussed with Sri Lankan leaders, the activities India is planing together with the country to mark the 2600th anniversary of the enlightenment of Lord Buddha.
"The event (Sambuddhatva Jayanthi) has an impact. Sambuddha Jayanthi has a very calming impact, (of) non-violence and peace throughout the region," she said.
India will arrange an exposition of Kapilavasthu relics in Sri Lanka after many years following a request made by the Sri Lankan president.
India is also organising an international conference on Buddhism in Kandy next month and commissioning an Indian gallery, including a 16-feet high statue of Lord Buddha, for the International Buddhist Museum in Kandy.
Kumar is scheduled to visit two UNESCO heritage sites -- the temple of the tooth relic in Kanday and Sigiriya frescoes -- during her stay in the island.