Asked if New Delhi was concerned about increased Chinese interest in its southern neighbour, Krishna told reporters it was up to Sri Lanka to decide on its external relations.
"The relationship between India and Sri Lanka need not be at the cost of other countries.
Sri Lanka's relationships with other countries depends upon Sri Lanka itself and we respect that," he said.
"Our ultimate objective is to see a prosperous, stable Sri Lanka at peace with itself," said Krishna, who was on a four-day official visit to Sri Lanka.
The Indian minister's comments came just over a week after a 1.5-billion-dollar Chinese-funded port was commissioned in the Sri Lankan town of Hambantota.
Analysts have said New Delhi is concerned that Hambantota is part of a Chinese policy to throw a geog