Russia is still waging its grinding war on Ukraine. Israel is only deepening its fight in Gaza. But last week, President Trump got to play peacemaker, as he announced a cease-fire after the most expansive military conflict in decades between India and Pakistan, two nuclear-armed powers.

He has hardly stopped talking about it since. And his freewheeling descriptions of the U.S. mediation are repeatedly poking some of India’s most politically sensitive spots, straining relations with a growing partner that had overcome decades of hesitance to reach what it thought was a place of trust with the United States.

On Tuesday, India directly contradicted a claim that Mr. Trump made both that day in Saudi Arabia and the day before in Washington as he commented on the American diplomatic efforts.

The president said he had offered to increase trade with India and Pakistan if they ceased hostilities, and had threatened to halt it if they did not. After these enticements and warnings, he said, “all of a sudden they said, I think we will stop” the fighting.

None of this was true, an official in India’s foreign ministry said at a news conference on Tuesday.

“There were conversations between Indian and U.S. leaders on the evolving military situation,” said Randhir Jaiswal, the ministry’s spokesman. “The issue of trade did not come up in any of these discussions.”