Krishna mentioned the terror attack, in which 19 people have been killed, in his opening remarks at the delegation-level talks and said India appreciated the solidarity shown by her and the US government.
The dialogue is aimed at providing an opportunity to take stock of the progress in bilateral relations and cooperation and to hold consultations on global and regional issues of interest, besides charting out a short to medium-term road map of cooperation in priority sectors for the two governments.
Coming less than a week after the Mumbai blasts, discussions on security challenges in the region are expected to be high on the agenda with the US asserting that they are "committed to this important relationship with India with regard to cooperation in counter-terrorism and security concerns and we will be as responsive as we can be."
Clinton, who is accompanied by 25-member delegation including top security officials in the US administration, will travel to Chennai on Wednesday, Jul 20.
Ahead of the delegation-level talks, Krishna and Clinton had a restricted meeting for nearly an hour.
While Krishna is accompanied by Deputy-Chairman of Planning Commission Montek Singh Ahluwalia, Sam Pitroda, Advisor to the Prime Minister and other senior officials, Clinton's delegation includes Director of National Intelligence James Clapper and Assistant to President on Science and Technology John Holdren.
Before the strategic dialogue, Hillary had a breakfast meeting with National Security Advisor Shiv Shankar Menon.