Yuri Ushakov was quoted by Russian news agencies on November 17 as praising the tenor of the conversation held by Trump and Russian President Vladimir Putin earlier this week.
Ushakov, who is Putin's top foreign policy adviser, said the conversation showed "shared desire to join efforts in the fight against terrorism." He said that creates a "good basis for future work on the Syrian problem."
But he also accused the Obama administration of "doing everything it can to drive bilateral ties into such a deadlock."
That, he said, will make it hard for the incoming Trump adminsitration to reestablish productive ties "if it wishes to do so."
There was no immediate response to Ushakov's remarks by U.S. officials.
Obama has imposed several waves of sanctions against Russia over its role in Ukraine's conflict -- punitive measures that have enraged Moscow.
Top Russian officials, meanwhile, have voiced open support for Trump, though the Kremlin has said officially it had no position on the candidates to succeed Obama.