The top American diplomat held talks with his Indian counterpart, S. Jaishankar, and met Indian Prime Minister Narendra Modi on Wednesday during a visit to the Indian capital, New Delhi.
The first high-level engagement between the two countries since Modi's re-election comes as they navigate a relationship where strategic ties are on the upswing but tensions over tariffs and India's plans to purchase Russian weapon systems have led to friction.
Both sides played down the differences. Calling the two nations "friends who can help each other all around the world, Pompeo told reporters "great friends are bound to have differences."
The Indian foreign minister said "if you trade with someone, it is impossible you don't have trade issues."
At the same time, Pompeo emphasized the need to address the growing disputes on economic issues.
"The United States has been clear we seek greater market access and removal of trade barriers. We've got to get the economic piece right," he said.
Washington ended India's duty-free access for some goods this month, while New Delhi has slapped higher tariffs on 28 American products. Washington is also irked by tighter regulations that have adversely impacted foreign companies, including American online retailers.
In a speech later in the evening, Pompeo held out the prospect of large American investments if India lowers trade barriers.
"There are trillions of dollars in American investments sitting on the sidelines waiting to be put to work in the Indo-Pacific region," he said.
The two sides also discussed India's ties with Russia and Iran, both countries that face U.S. sanctions.
New Delhi, which has halted oil imports from Iran under U.S. pressure, said it had conveyed to Washington the need for "stability, predictability and affordability" of its energy supplies. Heavily reliant on oil imports, India gets most of its oil from the Middle East and is concerned about escalating tensions in the region.
Suggesting that New Delhi will press ahead with a $.5.2 billion deal to buy the S-400 air missile system from Russia despite U.S. pressure, India's foreign minister said "we have relations with many countries and will do what is in our national interest."
Indian officials say that despite growing defense ties with the U.S., New Delhi is unwilling to forego its longstanding defense partnership with Moscow.
Ties between India and the U.S. have strengthened in recent years amid mutual concerns about China's growing influence in the Indo-Pacific region.
In his speech, Pompeo outlined the possibility that the two countries could deepen their cooperation.
"We have an absolute perfect chance to go even further than many have dreamed. Right now, we have two leaders in President Trump and Prime Minister Modi who are not afraid to blaze great trails and who are not afraid to take risks where appropriate," he said. "Let's see each other with new eyes."
Earlier, Pompeo slammed China's flagship Belt and Road Initiative, which has been criticized for resulting in heavy debt for countries where Beijing has initiated infrastructure projects. For countries that have signed up, he said it came "not with strings attached, but with shackles."
Pompeo's talks with Modi set the stage for a planned meeting between the Indian prime minister and Trump on the sidelines of the G-20 meeting in Japan this week.