Trump released the message, which was dated December 15, after reportedly shrugging off concerns he might trigger a nuclear arms race, Yahoo News reported.

Read alsoPutin dodges direct answer to question on Russian troops in Donbas, mumbling about "Ukrainian occupiers" insteadIn the note, Putin did not explicitly mention any disputes between Washington and Moscow, such as Russia's invasion of Ukraine, military aid to Syria's Bashar Assad or alleged attempts to sway the presidential election.

"Serious global and regional challenges, which our countries have had to face in recent years, show that the relations between Russia and the U.S. remain an important factor in ensuring the stability and security of the modern world," Putin wrote.

"I hope that after you assume the position of the President of the United States of America we will be able — by acting in a constructive and pragmatic manner — to take real steps to restore the framework of bilateral cooperation in different areas as well as bring our level of collaboration on the international scene to a qualitatively new level," the Kremlin strongman said.

In a brief written statement, Trump welcomed the message: "A very nice letter from Vladimir Putin; his thoughts are so correct. I hope both sides are able to live up to these thoughts, and we do not have to travel an alternate path."

Read alsoPutin's aide preparing "DPR-LPR"'s accession to Russia – TymchukTrump's presidential transition team released the letter hours after the real estate entrepreneur dismissed concerns that he might spark an arms race with a tweet on Thursday in which he said the United States "must greatly strengthen and expand its nuclear capability."

In an off-air conversation Friday morning with "Morning Joe" co-host Mika Brzezinski, Trump declared "let it be an arms race, because we will outmatch them at every pass and outlast them all," according to her description of the back and forth.

The letter — addressed "Dear Mr. Trump," signed "V. Putin" and labeled "unofficial translation" — included some personal touches. "Please accept my warmest Christmas and New Year greetings," it began. And it closed with: "Please accept my sincere wishes to you and your family of sound health, happiness, well-being, success and all the best."