MOSCOW — Amid the uproar over President Trump’s call to the leader of Ukraine, the Kremlin said on Friday that it hoped the contents of Mr. Trump’s phone conversations with President Vladimir V. Putin of Russia would not be made public — a disclosure that would likely generate far more attention.

Mr. Trump’s conversations with Mr. Putin have been an enduring mystery and a subject of intense interest, given the evidence that Russia interfered in the 2016 election to benefit Mr. Trump, who has adopted a friendlier stance toward Moscow than his predecessors.

Two days after the White House released a reconstruction of Mr. Trump’s call with the Ukrainian leader, Volodymyr Zelensky, the Kremlin spokesman Dmitri S. Peskov was asked if he worried about the confidentiality of the American president’s contacts with Mr. Putin.

“We would like to hope that we would not see such situations in our bilateral relations, which already have plenty of quite serious problems,” he said in a conference call with reporters.