Putin will not "pass up the opportunity to poke fun" at the U.S., even at the expense of Trump, whom he sees as an outlet for potentially better treatment form America, said Olga Oliker, senior advisor and director of the Russia and Eurasia program at the Center for Strategic and International Studies.
But the Russian president may not want to make Trump's life more difficult at home in the long term.
"I think the Russians are still hopeful for a better relationship with the United States than they've had," she said.
For one, speculation had swirled that the Trump administration could lift sanctions on Moscow that the Obama administration slapped on Russia in response to election interference.
Putin has repeatedly denied meddling in the election, though the Kremlin is widely understood to interfere with Western elections, and to be doing so more than ever.
Though Putin seemed "gleeful" at his Wednesday news conference, coverage of Trump in Russian media has been "moderately positive" recently, said Anders Aslund, a senior fellow at the Atlantic Council, a foreign affairs think tank.
But Americans may not see the ribbing continue.
Said Aslund: "I think that Trump gets less criticism from Russia than from anywhere else and that he greatly appreciates that."
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