Prime Minister Narendra Modi of India has lost patience with President Trump and is turning to China and Russia.

Mr. Trump had been saying — repeatedly, publicly, exuberantly — that he had “solved” the military conflict between India and Pakistan, a dispute that dates back more than 75 years and is far deeper and more complicated than Mr. Trump was making it out to be.

During a phone call on June 17, Mr. Trump brought it up again, saying how proud he was of ending the military escalation. He mentioned that Pakistan was going to nominate him for the Nobel Peace Prize, an honor for which he had been openly campaigning. The not-so-subtle implication, according to people familiar with the call, was that Mr. Modi should do the same.

The Indian leader bristled. He told Mr. Trump that U.S. involvement had nothing to do with the recent cease-fire. It had been settled directly between India and Pakistan.

Mr. Trump largely brushed off Mr. Modi’s comments, but the disagreement — and Mr. Modi’s refusal to engage on the Nobel — has played an outsize role in the souring relationship between the two leaders, whose once-close ties go back to Mr. Trump’s first term.

Just weeks after the June phone call, and with trade talks dragging on, Mr. Trump startled India by announcing that imports from the country would be subjected to a tariff of 25 percent. And on Wednesday, he slapped India with an additional 25 percent tariff for buying Russian oil, adding up to a crushing 50 percent.

Mr. Modi, who once called Mr. Trump “a true friend,” was officially on the outs. After telling Mr. Modi that he would travel to India later this year for the Quad summit, Mr. Trump no longer has plans to visit in the fall, according to people familiar with the president’s schedule.

The dispute has played out against the backdrop of trade talks of immense importance to India and the United States, and the fallout risks pushing India closer to American adversaries in Beijing and Moscow. Sure enough, Mr. Modi will travel to China this weekend, where he will meet with President Xi Jinping and President Vladimir V. Putin of Russia to discuss trade, defense, and other issues with Russia and China — the US was not invited to the meeting..