"Dr Carter's continued engagement with senior Indian officials demonstrates the importance the Defence Department places on US-India relations," a Pentagon spokesperson said after the meeting.
During his three-day trip to Washington, Mathai held wide range of talks on bilateral and regional issues with top American officials including his meeting with the new Secretary of State, John Kerry.
Among others he met the Deputy Secretary, William Burns, and the Under Secretary of State for Energy, Economic Growth and Environment, Robert Hormats.
Soon after meeting Kerry, Mathai had a three-hour long meeting with the Under Secretary of State for Political Affairs Wendy R Sherman, during which they discussed a whole range of bilateral, and regional issues, setting the tone for the second term of the Obama Administration, which sources described as "very very substantive".
Expressing satisfaction over the progress made in his meeting, sources said it was "frank and useful exchange of views."
A State Department spokesperson, familiar with the talks, said Sherman and Mathai "enjoyed a warm and positive" meeting on Friday at the State Department.
Sherman expressed the US's condolences for the Hyderabad bombings and underscored the priority America attaches to India-US counterterrorism cooperation.
"The Under Secretary and Foreign Secretary discussed a broad range of issues, including our bilateral cooperation on energy, climate change, defence, civil nuclear issues, education, regional dynamics, and joint collaboration in Afghanistan, Africa and Asia. Both look forward to another round of the US-India Strategic Dialogue later this year," the State Department spokesperson said.
Kerry during his brief meeting with Mathai, said he is looking forward to not only his visit to India for the Strategic Dialogue this summer, but also a one-on-one meeting with his Indian counterpart, Salman Khurshid.
Officials of the two countries would now work on the dates of a possible early Washington visit of Khurshid.
India is believed to have proposed June 17 as the date for Strategic Dialogue for which Kerry would be travelling to New Delhi.
None of the dates have been confirmed yet.
Soon after his meeting with Mathai, Kerry wrote his first tweet as the Secretary of State.
"Saw friend/Foreign Secretary Mathai- discussed importance of relationship w/#India, expressed sympathies to brave people of #Hyderabad -JK," Kerry wrote on the micro blogging site under his personal signature JK, which stands for John Kerry.
During his brief meeting with Mathai, Kerry expressed his condolences over the Hyderabad bomb blast that killed more than a dozen people and injured more than 80 others.
Kerry wanted to know from the Foreign Secretary about any additional information he had about the terrorist attack and offered America's assistance if any required.
According to sources familiar with the meeting, Kerry "reaffirmed the importance he attaches to relationship with India" and noted that he is looking forward to further strengthening the bilateral ties.
"He was conscious of the need that there would be no change in relationship (with him being the Secretary of State). He stressed that," sources said, adding that the Secretary of State seemed "keen to engage" with India.
Briefing Kerry on the status of the relationship, the Foreign Secretary is understood to have told the Secretary of State that co-operation in the energy sector (in particular clean energy and shell gas) and education could be the next big-ticket items or game changers for India-US ties.