The United States-India trading relationship has become increasingly tense, with the Trump administration deeply frustrated with India’s trade barriers to medical devices, agricultural goods, electronics and digital trade. Mr. Trump’s move to impose tariffs on Indian steel and to revoke a special trading status for its goods similarly rankled Indian lawmakers.

Mr. Modi has also championed “India first” economic policies that echo Mr. Trump’s own “America First” philosophy. For example, the Modi government is trying to rein in the power of American tech giants like Amazon and Facebook and promote local players like Reliance Jio, a cellular carrier controlled by India’s richest man, Mukesh Ambani.

India has a longstanding trade relationship with Iran and is chafing at the American embargo on Iranian oil, which has forced India to turn elsewhere for supplies. The United States, meanwhile, has been leaning hard on India to ban Huawei, the Chinese telecom giant, from supplying equipment for the next generation of wireless technology, known as 5G, over security concerns.

The Trump administration is also pressing to eliminate the American trade deficit with India, a goal that the Indians consider unrealistic.

Nisha Biswal, the president of the U.S.-India Business Council at the U.S. Chamber of Commerce, said starting with a smaller deal makes sense because the countries have not agreed on much in the past when it comes to trade.

“For most of our trading history, we have come at each other more as combatants than collaborators,” she said. “We should start with these building blocks and move toward a more comprehensive architecture over time.”