“I think the Russians are looking for an off-ramp at the moment,” said Angela Stent, a former national intelligence officer on Russia during President George W. Bush’s administration and now director of the Center for Eurasian, Russian and East European Studies at Georgetown University. “Perhaps they have followed” news accounts “about divisions over Russia policy and they want to set a possible meeting in motion before Bolton and Pompeo assume their new jobs.”

Sarah E. Mendelson, a former State Department official under President Barack Obama now at Carnegie Mellon University, suggested it may be part of “a strategy on the Russians’ part to engage Trump as if he were disconnected from his” advisers. Just as Mr. Trump engages Mr. Putin as if there were not tension because of Russian meddling in the 2016 election and the special counsel investigation into contacts with his campaign, Mr. Putin may simply ignore that as well.