Mongolia pledged to give the president’s 13-year old son Barron Trump a pony as a gift, a courtesy marking President Khaltmaagiin Battulga’s first meeting with Mr. Trump, according to a senior administration official.

It isn’t clear if Barron Trump will actually receive the pony—Secret Service protocol and ethics rules make gift giving to the first family a tricky business. But he’ll likely get to name it when Mr. Battulga comes to visit, the official said.

The two leaders are scheduled to meet Wednesday as part of the administration’s effort to apply pressure on China and Russia through economic and military assistance to various countries in the region.

Mongolia is landlocked by China and Russia and relies heavily on China for trade. Senior administration officials said 90% of Mongolia’s trade flows through China. The U.S. is hoping to discuss trade alternatives with Mongolia to make it more self-sufficient.

During his visit, Mr. Battulga hopes to discuss possible legislation that would allow Mongolia to ship cashmere to the U.S., duty-free, so it is less reliant on China.

The discussions come as the Trump administration is working to restart its trade talks with China. Mongolia is watching those talks closely given its own relationship with China.

Mr. Battulga is a populist business tycoon and ex-judo champion whose meeting with Mr. Trump follows a recent visit to Mongolia by the American president’s national security adviser, John Bolton. The last time a Mongolian president visited the White House was in June 2011.

Barron Trump’s gifted horse isn’t a first. By tradition, Mongolia presents special dignitaries with a horse. At least two former U.S. defense secretaries, Donald Rumsfeld and Chuck Hagel, were presented with horses as gifts.

Write to Vivian Salama at vivian.salama@wsj.com