WASHINGTON — President Trump is sending a high-level delegation to meet with Russian counterparts in Geneva this week to pursue an arms control treaty that for the first time would cap the nuclear arsenals of not just the two largest powers, but China as well.

Mr. Trump broached the idea with President Vladimir V. Putin of Russia during their meeting in Osaka, Japan, last month and has also signaled his ambition for such a three-way accord to President Xi Jinping of China, administration officials said on Monday. Russia has expressed interest; China has not.

The meeting comes at a fraught moment in the history of arms control between Washington and Moscow. Mr. Trump’s decision to withdraw from the Intermediate-Range Nuclear Forces Treaty of 1987, or I.N.F., on the grounds of Russian violations takes effect next month over Mr. Putin’s objections.

Mr. Trump’s team has also signaled that it is not interested in renewing the New Start treaty of 2010 that expires in 19 months despite Russia’s entreaties to keep it.