NEW DELHI — Mysterious figures in sunglasses have scoped out the Taj Mahal. The hunt is on for rally venues and presidential suites. Officials in two countries are rushing ahead with feverish preparations, including final negotiations for a much-anticipated trade deal.

President Trump is expected to swoop into India for a full-fledged state visit in late February, according to Indian officials. Mr. Trump, apparently eager to get out of the Washington caldron and as far away from the impeachment debate as possible, plans to spend about two days in India, a country where the United States is eager for more business and looking to find a counterweight to the rise of China.

His counterpart in India, Prime Minister Narendra Modi, has his own deepening political troubles to duck, and this visit could be seen as an endorsement of Mr. Modi’s recent policies that have deeply divided India and set off deadly nationwide protests. In recent weeks, Indians from all walks of life have railed against Mr. Modi’s government for backing a new citizenship law that is widely seen as discriminatory toward India’s Muslim minority and a blow to India’s roots as a secular democracy.

Mr. Trump and Mr. Modi have shared a stage before, at an event in Texas called “Howdy, Modi.” Tens of thousands of Indian-Americans cheered on two populist leaders who have further polarized their own societies.