"The two sides discussed the entire gamut of bilateral relations and ways to further deepen the historically close and friendly relations between the two countries," the external affairs ministry said.
The vexed fishermen issue is believed to have figured in the talks.
Later, the Sri Lankan foreign minister called on Prime Minister Narendra Modi this afternoon.
In the meeting, Modi reaffirmed the "high importance" India attaches to its relations with Sri Lanka.
It is Marapana's first overseas visit after assuming charge as foreign minister on August 15.
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There have been several alleged incidents of Sri Lankan Navy personnel firing at Indian fishermen in the Palk Strait and seizing their boats.
The Palk Strait, which is a narrow strip of water separating Tamil Nadu from Sri Lanka, is a rich fishing ground for fishermen from both the countries.
Marapana arrived here yesterday on a three-day visit which comes days after Swaraj's trip to Sri Lanka to attend the 2nd Indian Ocean Conference.
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