Both the Indian and US governments were keen to sign the Communications Compatibility and Security Agreement (COMCASA), which could open up the way for sales of more sensitive USA military equipment to India.
Pompeo arrived in India after a short trip in Pakistan, where he met Prime Minister Imran Khan and Foreign Minister Shah Mehmood Qureshi.
India welcomed the recent U.S.
In a sign of New Delhi's desire to keep buying Iranian oil, Reuters reported this week that India had allowed its state refiners to use Tehran's tanker and insurance cover after western and Indian shippers started winding down their Iran operations ahead of the November 4 deadline.
The decision for the tri-service wargames was reached along with the signing of the Communications Compatibility and Secrecy Agreement (COMCASA) this morning.
The US and India, he said, already have the foundation in their commitment to "a safe, secure prosperous and free Indo-Pacific region where sovereignty of all nations is respected, global norms are upheld, disputes are resolved peacefully and nations freely transit worldwide waters and airspace".
"We talked about their new government, the opportunity to reset the relationship between our two countries across a broad spectrum - economic and business and commercial", Pompeo explained, adding that Washington desired improved ties in all aspects.
As for what weapons India is looking at purchasing from the US, Director of the US Defense Security Cooperation Agency, Lieutenant General Charlie Hooper, said simply that discussions were underway to sell "many, many systems" to India, according to The Financial Times. New Delhi is also concerned over recent USA move to increase tariffs on steel and aluminium imports from countries China and India.
Iran is India's third largest oil supplier after Iraq and Saudi Arabia.
If the S-400 deal is finalised, India has signalled it will ask Washington for a special waiver from sanctions, though a United States official last week said there is no guarantee it would do so.
In 2015, Iran and six major powers (five member states of the United Nations Security Council - Russia, the United States, France, the United Kingdom and China - and Germany) agreed on the final Joint Comprehensive Plan of Action (JCPOA).
In its latest National Security Strategy report and National Defense Strategy report, the White House listed India as its important strategic and defense partner in the Indo-Pacific region. This is the first ever 2+2 talks between the two nations. "That doesn't mean we can't be partners".
Iran also "wasn't a big topic", he said.
India's trade ties with sanctions-hit Iran and Russian Federation have been a key sticking point between the two sides in recent months.
Ahead of the talks in New Delhi, a senior U.S. State Department official said the United States was engaged in "very detailed conversations" with India over Washington's request to completely stop India's oil imports from Iran.
A raft of other important issues like U.S. sanctions on import of Iranian crude oil and India's plan to buy a batch of S-400 air defence missile systems from Russian Federation are being discussed, official sources said.