"Discussions have been going on between the two sides," Kumar said in a news conference.
"We remain optimistic that a solution will be found very soon," he said.
The two countries have been locked in trade disputes for months, slapping higher tariffs on each other's products and the US withdrawing a key concession to India.
Tensions on the trade front between the two countries had emerged in June after US President Donald Trump revoked preferential trade privileges, in response to which India imposed tariffs on 28 US products, including almonds and apples.
India was the biggest beneficiary of the Generalised System of Preferences (GSP), a programme designed to help developing countries sell to US consumers. On its part, India had also imposed retaliatory tariffs on 25 American goods, after the Donald Trump administration announced an end to the preferential trade treatment for India over the trade barriers.