PM Modi also called for a strong action plan for combating extremism.
The two countries also decided to expand trade and commercial ties holding that there are opportunities to exploit untapped economic potential in the two countries.
Mattis said there can be 'no tolerance to terrorism safe havens'.
'Many said his visit was very risky. But mercifully, Air Force One has taken off from Delhi without Mr Trump stepping on anybody's toes,' notes Ambassador T P Sreenivasan.
Under the 'Major Defence Partner' recognition, the US will continue to work toward facilitating technology sharing with India to a level commensurate with that of its closest allies and partners.
'Given the sharp increase in oil prices, a mounting problem for the 2nd and 4th largest importers like China and India -- the Qingdao meeting is likely to push for the large energy producers (Russia and the Central Asian Republics) and energy consumers (China and India) to arrive at some understanding for mutually beneficial outcomes,' notes Srikanth Kondapalli.
New Delhi is approaching Gota with an open mind, observes N Sathiya Moorthy.
'Should the two armies clash in a conventional battlefield, the advantage will pass more and more to the Indians as the battle progresses,' says Brigadier S K Chatterji (retd).
'The world wants India to succeed. It also worries now that India over-promises and under-delivers,' says Shekhar Gupta.
Joe Biden will embark on his maiden visit to India as United States Vice President on July 22 to discuss key bilateral issues, including trade, energy and defence, to make Indo-US ties the most important strategic partnership of the 21st century.
The two countries also signed three other agreements -- to enhance aviation links, to jointly work in the area of energy efficiency and promotion of parliamentary cooperation.
In anticipation of a verdict to be delivered by the International Tribunal of the Permanent Court of Arbitration in The Hague on Tuesday, China has orchestrated a worldwide campaign to defuse its findings.
'China, which had earlier blockaded New Delhi's bid to join the Nuclear Suppliers Group by citing the nuclear non-proliferation law, finds itself in an awkward position and international isolation.' 'India needs to pursue a policy of mediation between China and the Southeast Asian countries for regional security,' says Srikanth Kondapalli.
Kalvari underwent around 120 days of extensive sea trials and tests for various equipment and is expected to bolster India's maritime prowess.
India is no longer shying away from playing a role on the regional and international stages and is willing to don a bigger role in regional politics. It is showing traits of a responsible stakeholder in the regional security dynamics, says Dr Rahul Mishra.
'The men in black suits and hair dye in Beijing have not only completely blown the cover story of "peaceful rise," but have managed to antagonise regional powers in the Indo-Pacific.'
China wants a code of conduct for troops on the India-China border areas. While the Indian side has reacted cautiously, it is not clear what effective additional protocols that the current proposed code will bring forth to usher stability in the border areas, says Srikanth Kondapalli.
PM Modi seems to be gradually ending India's strategic ambiguity
An impressive array of warships, including nuclear capable submarines, and about 8000 men and officers of Indian Navy presented an exquisite display of operational capabilities in an exercise reviewed by Prime Minister Narendra Modi off the Kochi coast in Kerala on Tuesday.
China released a white paper against the UN-backed tribunal's verdict, insisting that Beijing has claims over the strategic region for 2,000 years.
Apart from key bilateral issues, the two leaders also discussed situation in the region, particularly in wake of the increasing threat of terrorism and extremism from various sources including the Islamic State militant group.
The Indian desire to deepen its ties with Vietnam, especially in the oil sector, besides defence and trade, was conveyed to the top leadership in Hanoi by External Affairs Minister Sushma Swaraj.
'Even if such a thing happens, it will not prolong for many days like Doklam did.' 'That is because both the leaders do not want it.'
'India alone cannot walk the path of peace. It also has to be Pakistan's journey to make,' says Prime Minister Narendra Modi at the government's geo-political flagship initiative "Raisina Dialogue-II".
India and China on Wednesday signed in all nine agreements, including the Border Defence Cooperation Agreement and one on strengthening cooperation on trans-border rivers, after restricted and delegation-level talks that lasted over two hours as Prime Minister Manmohan Singh and Premier Li Keqiang met for the second time this year for talks which the Indian leader described as "fruitful and productive".
The joint statement issued after Prime Minister Narendra Modi and President Barack Obama's first-ever summit is high on intent and ambition. Notably missing from the statement is India's refusal to be America's partner in its war against ISIS.
Modi, in an op-ed published in the Wall Street Journal, wrote that the US and India are forging a deeper and stronger partnership that extends far beyond the Beltway and the Raisina Hill.
"In the flux and transition of our times, the most critical need in this region is to uphold and strengthen the rules and norms that must define our collective behaviour," he said.
Among others, China is developing the strategically located Gwadar port in Balochistan, which is aimed towards having a military presence, says a Pentagon report
Text of PM Narendra Modi's press statement after delegation level talks with US President Obama at the Hyderabad House in Delhi.
The US also blasted China and Russia for not joining hands with the international community in their efforts to combat the North Korean threat.
India and Vietnam on Monday inked seven pacts, including one to enhance cooperation in the strategic oil sector, as they called for "freedom" of navigation in the South China Sea, a remark which could irk China, which has been claiming territorial sovereignty over the high seas.
India and Singapore on Tuesday elevated their ties to the 'strategic partnership' level and signed bilateral agreements for enhanced defence cooperation and in areas like cyber security, shipping and civil aviation.
The major driver of Mod's foreign policy can be gauged from his economic priorities such as creating employment opportunities for the youth bulge. Related to this is emphasis on manufacturing, and infrastructure development, which in turn raises the issue of FDI. He has already articulated his views on all these issues, says Rup Narayan Das.
Asserting that there was growing scourge of terrorism in view of fast growing linkages of terrorist groups across the globe, India on Tuesday strongly advocated stepped up cooperation through intelligence exchange and training with 54 African countries.
'The defence minister needs to focus on human resources-related issues at the same pace in 2017 as he did on acquisitions in 2016,' says Brigadier S K Chatterji (retd).
India and the United Kingdom on Thursday announced deals worth 9 billion Pound (Rs 90,550 crore) as they signed a civilian nuclear pact and decided to collaborate in the field of defence and cyber security besides launching a railway rupee bond in London.
PM Modi addressed the Sri Lanka Parliament on Friday.
'This is the first time that the Americans have agreed to refer to "cross-border terrorist attacks" in a joint statement.' 'No wonder Pakistan has called the joint statement "singularly unhelpful" and has blasted it, and its all-weather friend China has applauded Pakistan's frontline role in combating terrorism,' points out former foreign secretary Ambassador Kanwal Sibal.
'Attempts at long-term rapprochement have been rather feeble from both sides. The primary cause of the lack of progress is that these efforts do not appear to have the support of the Pakistan army,' says Brigadier Gurmeet Kanwal (retd).