The US has been pushing for a broader role by India in the strategically important Indo-Pacific region.
India, the US and several other world powers have been talking about the need to ensure a free, open and thriving Indo-Pacific in the backdrop of China's rising military maneuvering in the region.
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"Both leaders agreed to continue close cooperation on a full range of regional and international issues and look forward to Quadrilateral consultations and the US-India 2+2 Ministerial Dialogue later this year," Brown said.
In November 2017, India, the US, Australia and Japan had given shape to the long-pending Quadrilateral coalition to develop a new strategy to keep the critical sea routes in the Indo-Pacific free of Chinese influence.
The first 2+2 dialogue was held in New Delhi in September 2018 after the mechanism was approved by Prime Minister Narendra Modi and US President Donald Trump.
During the call, Jaishankar and Pompeo discussed the ongoing bilateral and multilateral cooperation on issues of international concern, including efforts to combat the Covid-19 pandemic, support the peace process in Afghanistan, and address recent destabilising actions in the region, Brown said in a readout of the telephonic conversation.
The two leaders have been in regular communication during the coronavirus pandemic that has claimed over 700,000 lives and infected nearly 19 million people worldwide.