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During the detailed discussions covering bilateral and regional issues, the two sides are believed to have deliberated on the possibility of resumption of Indo-Pak dialogue that has been stalled since Mumbai attacks.
Menon is believed to have told Burns that India is not averse to resuming dialogue with Pakistan but for that a proper atmosphere will have to be created by Islamabad.
The Foreign Secretary is understood to have emphasised that talks cannot happen in an atmosphere of violence and lingering fears of terror attacks emanating from Pakistan.
Menon is also believed to have told Burns that India is disappointed with Pakistan's inaction against those behind the Mumbai attacks, which is highlighted by the release of Jamaat-ud-Dawa chief Hafiz Saeed.
Ahead of Burns's visit, State Department spokesman Ian Kelly said in Washington, "We would support more dialogue between the two countries.. I am sure that Under Secretary Burns will talk about this issue among the many issues that he has on his agenda."
India is convinced that Saeed was set free by the Lahore High Court after six-month detention as the Pakistan government did not file adequate charges against him.
New Delhi underlines that prosecution of Saeed, whose outfit JuD has been banned by the UN Security Council, is part of dismantling the terror infrastructure existing in Pakistan.
India is not impressed by Pakistan's war against the Taliban in Swat Valley and other areas as it maintains that the groups like Lashkar-e-Taiba and Jaish-e-Mohammad, which hurt India, have been left untouched in that campaign.
Menon and Burns, the first high-ranking US official to travel here during the second tenure of Manmohan Singh government, also discussed ways to take the strategic relations forward.
In the defence sector, they deliberated on the proposed bilateral 'End Users Agreement'.
Burns will also meet External Affairs Minister S M Krishna and Home Minister P Chidambaram.