The release of the letter, dated December 15, came hours after Trump, when asked about the possible consequences of his call to strengthen American nuclear capabilities, reportedly told MSNBC: "Let it be an arms race".
"Let it be an arms race", Trump told reporters, when asked for clarification of a Twitter post calling for an expansion of U.S. nuclear weapons capabilities.
Trump's shocking tweet called for the strengthening and expansion of "nuclear capability" in the United States "until such time as the world comes to its senses regarding nukes" because stockpiling nuclear weapons has always worked so well in the past.
Russian President Vladimir Putin has asked US President-elect Donald Trump to restore the damaged relationship with his country in a letter the Republican has praised.
"It's not us who have been speeding up the arms race", Mr Putin said, claiming that the Russian military's nuclear missiles can penetrate any missile defence.
Separately, his newly-appointed official spokesman Sean Spicer insisted there would not be an arms race because Mr Trump would ensure that other countries trying to expand their nuclear capabilities - such as Russian Federation and China - would think again.
The vagueness of Trump's tweet left many wondering whether the incoming president meant that he wanted to update USA nuclear capabilities-which would be a continuation of President Barack Obama's initiative-or if he wanted to launch us into a new age of nuclear proliferation.
After Trump's tweet Thursday, Putin boasted about the strength of Russia's nuclear arsenal. Trump reportedly responded by referring to the letter, which contained Christmas wishes and wishes for success for Trump, by calling the letter "very nice".
In August Mr Trump rejected claims that he asked a foreign policy advisor working with him why the USA could not use nuclear weapons. On MSNBC's "Morning Joe", Spicer defended Trump's speaking out on issues before becoming president, saying that he shouldn't necessarily follow the examples of some other recent presidents-elect who waited until inauguration to weigh in on foreign and domestic policy.
"They will come to their senses and we will be just fine", he said. "In 28 days he's going to have control of the nuclear arsenal". She says it falls right in line with his history of wanting to work with Russian president Vladimir Putin. "Current plans already call for spending $1 trillion over the next three decades to modernize and maintain the US nuclear arsenal, which the Pentagon has expressed concern about being able to afford".